Question

The side lengths of the following right triangle 15,20 and 25, as shown below. The altitude from the right angle splits the hypotenuse into line segments of length x and y. Solve for h,x, and y.

Answer 1

`h = 12`

`x = 9`

`y= 16`

Explanation:

Given

The attached triangle

Required

Find h, x and y

Let the base of the triangle be 15.

So, the area is:

`A = (1)/(2) * 15 * 20`

`i.e\ height = 20`

`A = (1)/(2) * 300`

`A = 150`

Let the base of the triangle be 25.

So, the area is:

`A = (1)/(2) * 25 * h`

`i.e\ height = h`

`A = (1)/(2) * 25h`

Substitute
`A = 150`

`(1)/(2)*25h = 150`

Solve for h

`h = (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`