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Pepsi [2]
2 years ago
10

The side lengths of the following right triangle 15,20 and 25, as shown below. The altitude from the right angle splits the hypo

tenuse into line segments of length x and y. Solve for h,x, and y.

Mathematics
1 answer:
kompoz [17]2 years ago
7 0

Answer:

h = 12

x = 9

y= 16

Step-by-step explanation:

Given

The attached triangle

Required

Find h, x and y

Let the base of the triangle be 15.

So, the area is:

A = \frac{1}{2} * 15 * 20

i.e\ height = 20

A = \frac{1}{2} * 300

A = 150

Let the base of the triangle be 25.

So, the area is:

A = \frac{1}{2}  * 25 * h

i.e\ height = h

A = \frac{1}{2}  * 25h

Substitute A = 150

\frac{1}{2}*25h = 150

Solve for h

h = \frac{150 *2}{25}

h = 6 *2

h = 12

Considering the smallest triangle

Hypotenuse = 15

So:

15^2 = h^2 + x^2

15^2 = 12^2 + x^2

This gives:

15^2 - 12^2 = x^2

81 = x^2

Take square roots

9 =x

x = 9

Solving for y

x + y = 25

y= 25 - x

y= 25 - 9

y= 16

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