Let ABC be a triangle such that AB=13 BC=14 and CA=15. D is a point on BC such that AD Bisects
Answers
Answer:
Area of triangle ADC is 54 square unit
Step-by-step explanation:
Here is the complete question:
Let ABC be a triangle such that AB=13, BC=14, and CA=15. D is a point on BC such that AD bisects angle A. Find the area of triangle ADC .
Step-by-step explanation:
Please see the attachment below for an illustrative diagram
Considering the diagram,
BC = BD + DC = 14
Let BD be [tex]x[/tex] ; hence, DC will be [tex]14-x[/tex]
and AD be [tex]y[/tex]
To, find the area of triangle ADC
Area of triangle ADC = [tex]\frac{1}{2} (DC)(AD)[/tex]
= [tex]\frac{1}{2}(14-x)(y)[/tex]
We will have to determine [tex]x[/tex] and [tex]y[/tex]
First we will find the area of triangle ABC
The area of triangle ABC can be determined using the Heron's formula.
Given a triangle with a,b, and c
[tex]Area =\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where [tex]s = \frac{a+b+c}{2}[/tex]
For the given triangle ABC
Let [tex]a[/tex] = AB, [tex]b[/tex] = BC, and [tex]c[/tex] = CA
Hence, [tex]a = 13, b= 14,[/tex] and [tex]c = 15[/tex]
∴ [tex]s = \frac{13+14+15}{2} \\s= \frac{42}{2}\\s = 21[/tex]
Then,
Area of triangle ABC = [tex]\sqrt{(21)(21-13)(21-14)(21-15)}[/tex]
Area of triangle ABC = [tex]\sqrt{(21)(8)(7)(6)}[/tex] = [tex]\sqrt{7056}[/tex]
Area of triangle ABC = 84 square unit
Now, considering the diagram
Area of triangle ABC = Area of triangle ADB + Area of triangle ADC
Area of triangle ADB = [tex]\frac{1}{2} (BD)(AD)[/tex]
Area of triangle ADB = [tex]\frac{1}{2}(x)(y)[/tex]
Hence,
Area of triangle ABC = [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]
84 = [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]
∴ [tex]84 = \frac{1}{2}(xy) + 7y - \frac{1}{2}(xy)[/tex]
[tex]84 = 7y\\y = \frac{84}{7}[/tex]
∴ [tex]y = 12[/tex]
Hence, [tex]y =[/tex] AD = 12
Now, we can find BD
Considering triangle ADB,
From Pythagorean theorem,
/AB/² = /AD/² + /BD/²
∴13² = 12² + /BD/²
/BD/² = 169 - 144
/BD/ = [tex]\sqrt{25}[/tex]
/BD/ = 5
But, BD + DC = 14
Then, DC = 14 - BD = 14 - 5
BD = 9
Now, we can find the area of triangle ADC
Area of triangle ADC = [tex]\frac{1}{2} (DC)(AD)[/tex]
Area of triangle ADC = [tex]\frac{1}{2} (9)(12)[/tex]
Area of triangle ADC = 9 × 6
Area of triangle ADC = 54 square unit
Hence, Area of triangle ADC is 54 square unit.
Related Questions
A woman making $3000 per month has her salary reduced by 10% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 20% raise over her reduced salary. Find her salary after the raise.
Answers
Answer:
$3240 a month
Step-by-step explanation:
First, find her reduced salary:
3000(0.9)
= 2700
Then, find her salary after the raise:
2700(1.2)
= 3240
So, her salary after the raise is $3240 a month
Solve the literal equation 5a + 10b = 2b - 4a for a.
Answers
Answer:
A=-8b/9
Step-by-step explanation:
How do you write 582,030 in expanded form
Answers
Answer:
500,000 + 80,000 + 2,000 + 30
In training for a swim meet, Logan swam 750 meters in 1/3 of an hour. His swimming partner, Mila, swam 2/3 of Logan's distance in 1/4of an hour. What is Mila's average swimming speed?
Answers
Answer: 2000m/h
Step-by-step explanation:
speed = distance/time
milas distance was (2/3).(750 m) = 500 m, so her speed was (500 m)/(1/4) = 2000 m/h
Anjali spent half of her weekly allowance
at the movies. To earn more money her
parents let her weed the garden for $10.
What is her weekly allowance if she ended
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Answers
Which of the following is a value are perfect square
Check all that apply
1
2
55
81
121
Answers
Answer:
1, 81, and 121 are correct
Step-by-step explanation:
they are the only ones that do not have a decimal when squared
1=1
81=9
121=11
1x1=1, so it is technically a perfect square. 81 is a perfect square because 9 can be multiplied by 9 to get 81. 121 is a perfect square for the same reason- 11 can be multiplied by itself to get 121
What are the different types of cardinal numbers?
Answers
Answer:
Cardinal, Ordinal, and Nominal Numbers
Step-by-step explanation:
Answer:
A Cardinal Number is a number that says how many of something there are, such as one, two, three, four, five. An Ordinal Number is a number that tells the position of something in a list, such as 1st, 2nd, 3rd, 4th, 5th etc
Find the missing exponent
Answers
Answer:
-6
Step-by-step explanation:
When an exponent is outside and inside the parenthesis you need to add them to get rid of the the parenthesis. The answer is -6 because -6*2 is -12.
Hope this helps. If you have questions put them in the comments.
Answer:-6
Step-by-step explanation:
When an exponent is outside and inside the parenthesis you need to add them to get rid of the the parenthesis. The answer is -6 because -6*2 is -12.
round 737.88 to the nearest tenth place?
Answers
Answer:
737.9
Step-by-step explanation:
8 is the hundredth place in 737.88, and 8 rounds up. So, the answer is 737.9
Answer:
737.9
Step-by-step explanation:
When we round something to the nearest ___ place, we want to look to the value to the right of it.
Since we're rounding it to the nearest tenths place, we want to look at the value to the right of it - the hundredths place.
The number in the tens place will be one more if the hundredths place is 5 or greater. It will remain the same if the hundredths place is below 5.
8 is greater than 5. This means the tens place will round up to 9.
So 737.9.
Hope this helped!
If a package of gift cards has a total value of $1050 how much does the average set of 2 gifts card price at if there are 15 in a group?
Answers
Answer:
$140
Step-by-step explanation:
If a package of gift cards has a total value of $1050, the total price for 2 gift cards will be 2×$1050 = $2100
If there are 15 in an average set of 2 gift cards, the average cost of the two gift cards will be expressed as;
Total price of 2gift cards/amount of card per group.
Average cost of of 2 gift cards = $2100/15
= $140
Hence the average cost of 2gift cards if there are 15 in a group is $134
Algebra 2 Help! Please help.
Answers
Step-by-step explanation:
h(x) =-x-4
h(x)=9
=>9=-x-4
=>x=-13
Answer:
We place 9 in the first expression instead of h (x)
Then we solve the equation
9=-x-4
x=-13
Color of car driven:___________.Is the variable qualitative or quantitative? A. The variable is qualitative because color is found by measuring or counting. B. The variable is qualitative because color describes an attribute or characteristic. C. The variable is quantitative because color describes an attribute or characteristic. D. The variable is quantitative because color is found by measuring or counting.
Answers
Answer:
B. The variable is qualitative because color describes an attribute or characteristic.
Step-by-step explanation:
Color is a qualitative variable, used to describe an object. Color cannot be measure or counted, but can be used as a descriptive property of an object. Other examples of qualitative variables include beauty, happiness etc
Quantitative variables are those that can be counted or measure. examples of quantitative variables are height. age, weight, loudness, etc
What’s the answer to 1.9m + 14 = 2m?
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{m = 140}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{1.9m + 14 = 2m}[/tex]
Move 2m to right hand side and change it's sign
Similarly, move 14 to left hand side and change it's sign
[tex] \dashrightarrow{ \sf{1.9m - 2m = - 14}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{ - 0.1m = - 14}}[/tex]
Divide both sides by -0.1
[tex] \dashrightarrow{ \sf{ \frac{ - 0.1m} { - 0.1} = \frac{ - 14}{ - 0.1}}} [/tex]
Calculate
[tex] \dashrightarrow{ \sf{m = 140}}[/tex]
Hope I helped!
Best regards! :D
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Answers
Answer:
the answer is 1649
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
2x + 3y = 29
x = 4
A. (4,7)
B. (3,2)
C. (7,4)
D. (4,11)
Answers
3x^4-7x^2+11 Expression
Answers
Which of the following statements correctly describes the expression below based on its degree and number of terms? 3x^4 - 7x^2 + 11. The expression has four terms and a degree of 6. The expression is a trinomial with a degree of 6. The expression is a trinomial with a degree of 4. The expression has four terms and a degree of 4.
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what is the reciprocal of 4 over 5
Answers
As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected:
Monthly fixed cost (loan payment, taxes, insurance, maintenance) $6000
Variable cost per occupied room per night $ 20
Revenue per occupied room per night $ 75
a. Write the expression for total cost per month. Assume 30 days per month.
b. Write the expression for total revenue per month, first using the general variables, and second including the values of known variables).
c. If there are 12 guest rooms available, can they break even? What would be the profit with 12 rooms?
d. What percentage of rooms would need to be occupied, on average, to break even?
Answers
Answer:
Instructions are below.
Step-by-step explanation:
Giving the following information:
Monthly fixed cost= $6,000
Variable cost per occupied room per night= $20
Revenue per occupied room per night= $75
First, we need to structure the total cost formula:
Total cost= 6,000 + 20*x
x= occupied room
Now, we can find the expression for total revenue:
Revenue= selling price per unit*units - fixed cost - unitary variable cost*units
Revenue= 75*x - 6,000 - 20*x
I assume that the 12 rooms will be occupied for the 30 days:
Revenue= 75*(12*30) - 6,000 - 20*(12*30)
Revenue= $13,800
Finally, we need to determine the break-even point in units:
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 6,000 / (75 - 20)
Break-even point in units= 109 rooms
On percentage= (109/360)*100= 30.28%
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Answers
Answer:
tththtfhhtfhtfttfh
Step-by-step explanation:
tfhtfh
Answer:
0
Step-by-step explanation:
The question is asking for any number between -5 and 2, so you can choose -4, -3, -2, -1, 0, or 1
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Answers
Answer:
x + 6 = 3
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Step-by-step explanation:
x + 6 = 3
x + 6 - 6 = 3 - 6
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pls help i will mark brainliest......i have a time limit
Answers
Answer:
Hey there!
If angle one is congruent to angle two, all of the above is true.
Let me know if this helps :)
Express the following vector in the form v vi+V2j+ v3k 3u -v if u (3,5,-8) and v (2,-5,7)
Answers
Answer:
7i+20j-31kStep-by-step explanation:
Given the vectors u (3,5,-8) and v (2,-5,7), they can also be written as;
u = 3i+5j-8k
v = 2i-5j+7k
To express the vector 3u - v in vector form, first let us find the vector 3u;
3u = 3(3i+5j-8k)
3u = 3(3i)+3(5j)-3(8k)
3u = 9i+15j-24k
Subtract v from the resulting vector.
Since v = 2i-5j+7k
3u - v = 9i+15j-24k - (2i-5j+7k)
3u-v = 9i+15j-24k -2i+5j-7k
collect the like terms
3u-v = 9i-2i+15j+5j-24k-7k
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OLGA went on an 82 mile bike trip last week by Thursday night she travel 64 miles of the total distance which president is reasonable estimate of how much of the trip OLGA completed by Thursday
Answers
Answer:Note: This symbol ≈ means approximately.
629 ≈ 600
215 ≈ 200
111 ≈ 100
588 ≈ 600
Now, we add the simplified numbers up: 600 + 200 + 100 + 600 = 1500. So, your answer is D or 1,500.
Step-by-step explanation:PLZZZ GIVE BRAINLYEST HOPE IT HELPS
Find an expression for the number of colored border tiles needed for any N x N square center.
Answers
Answer:
8N - 4 border tiles.
Step-by-step explanation:
There are 4 border tiles in each corner and between the tiles there are N-2 tiles along the 4 sides.
So the number of border tiles
= 4+ 4(N - 2)
= 4 + 4N - 8
= 8N - 4.
Which is the best estimate of 47 to the nearest tenth?i
Answers
Answer:
47.0Step-by-step explanation:
Answer:
Square Root of 47 to the nearest tenth, means to calculate the square root of 47 where the answer should only have one number after the decimal point. To check that the answer is correct, use your calculator to confirm that 6.92 is about 47.
Step-by-step explanation:
Plz Mark me as brainliest
1/2 of 24 =
1/6 of 24
1/4 of 24 =
Answers
Answer:
1/2 of 24 = 12
1/6 of 24= 4
1/4 of 24 = 6
Step-by-step explanation:
divide
1/25, 1/4 , 0.2 least to greatest
Answers
Answer:
1/25 0.2 1/4
Step-by-step explanation:
1/25, 1/4 , 0.2
1/25 = 0.04
1/4 = 0.25
1/25 0.2 1/4
There are 360 degrees in a circle. How many arc seconds will be in 96 % of a circle?
Answers
What is 1/5 miles in units to 1/65 hours
Answers
Answer:
13/65 miles in 1/65 of an hour, I believe is the answer you're looking for. Hope this helped!
Step-by-step explanation:
if a bag contains 12 quarts 6 dimes 18 nickles what is the part to whole ratio of dimes to all coins
Answers
Answer:
I'm not really sure but I think its 6:36
Step-by-step explanation:
12 quarters + 18 nickels + 6 dimes = 36 coins in total
6 dimes in total
6:36