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1.What is the value of x?


2.What is the value of x?
Enter your answer as a decimal.

3.What is the value of x?

4.What is the value of x?


5.The area of a right triangle is 210 in². The height of the right triangle is 35 in.

What is the length of the hypotenuse of the right triangle?

Enter your answer in the box.

1What is the value of x 2What is the value of x Enter your answer as a decimal 3What is the value of x 4What is the value of x 5The area of a right triangle is class=
1What is the value of x 2What is the value of x Enter your answer as a decimal 3What is the value of x 4What is the value of x 5The area of a right triangle is class=
1What is the value of x 2What is the value of x Enter your answer as a decimal 3What is the value of x 4What is the value of x 5The area of a right triangle is class=
1What is the value of x 2What is the value of x Enter your answer as a decimal 3What is the value of x 4What is the value of x 5The area of a right triangle is class=

Respuesta :

Problem 1)

Let p = distance from V to Y

By the angle bisector theorem, we can form the proportion

VT/VY = TK/KY
57/p = 129.2/68
57*68 = p*129.2
3876 = 129.2p
3876/129.2 = 129.2p/129.2
30 = p
p = 30

Use the value of p to find x
x = VY+YK
x = p+68
x = 30+68
x = 98


Answer: 98 mm

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Problem 2)

The triangles are similar, so we can form a proportion of the corresponding sides

MN/MA = MP/MB
67.2/(67.2-32) = 81.9/x
67.2/35.2 = 81.9/x
67.2*x = 35.2*81.9
67.2*x = 2882.88
67.2*x/67.2 = 2882.88/67.2
x = 42.9


Answer: 42.9 meters

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Problem 3)

Similar to problem 1, we use the same theorem

EG/GD = EH/HD
44.8/(x+4) = 56/35
44.8*35 = 56(x+4)
1568 = 56x+224
1568-224 = 56x+224-224
1344 = 56x
56x = 1344
56x/56 = 1344/56
x = 24


Answer: 24 millimeters

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Problem 4)

We'll use a similar idea used in problem 2

9/(9+72) = (3x-20)/((3x-20)+56)
9/81 = (3x-20)/(3x+36)
1/9 = (3x-20)/(3x+36)
1*(3x+36) = 9(3x-20)
3x+36 = 27x-180
3x+36+180 = 27x-180+180
3x+216 = 27x
3x+216-3x = 27x-3x
216 = 24x
24x = 216
24x/24 = 216/24
x = 9


Answer: 9 centimeters

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Problem 5) 

Area of triangle
A = 0.5*b*h

Plug in A = 210 and h = 35; solve for b
A = 0.5*b*h
210 = 0.5*b*35
210 = 0.5*35*b
210 = 17.5*b
12 = b
b = 12

Now use the base and height to find the hypotenuse

a^2 + b^2 = c^2
h^2 + b^2 = c^2
35^2 + 12^2 = c^2
1369 = c^2
c^2 = 1369
sqrt(c^2) = sqrt(1369)
c = 37


Answer: 37 inches

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