Question

A reflecting pool is shaped like a right triangle with one leg along the wall of a building. The hypotenuse is 9feet longer than the side along the building. The third side is 7feet longer than the side along the building. Find the lengths of all three sides of the reflecting pool.

Answer 1

The length of the leg along the wall of the right triangle is 8 feet

The length of the hypotenuse of the right triangle is 17 feet

The length of the other leg (third side) of the right triangle is 15 feet

Explanation:

Let

x ----> the leg along the wall of the right triangle

y-----> the hypotenuse of the right triangle

z ----> the other leg (third side) of the right triangle

we know that

`y=x+9` ----> equation A

`z=x+7` ----> equation B

Applying the Pythagorean Theorem

`y^2=x^2+z^2` ----> equation C

Solve the system by substitution

substitute equation A and equation B in equation C

`(x+9)^2=x^2+(x+7)^2`

solve for x

`x^2+18x+81=x^2+x^2+14x+49\\2x^2-x^2+14x-18x+49-81=0\\x^2-4x-32=0`

Solve the quadratic equation by graphing

using a graphing tool

The solution is x=8

see the attached figure

Find the value of y

`y=8+9=17\ ft`

Find the value of z

`z=8+7=15\ ft`

therefore

The length of the leg along the wall of the right triangle is 8 feet

The length of the hypotenuse of the right triangle is 17 feet

The length of the other leg (third side) of the right triangle is 15 feet