I have a math question just trying to see if someone could help

Question

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

Answer 1

Right triangles have the following relationship between their legs and hypotenuse where a and b are the lengths of the legs and c is the length of the hypotenuse:

a^2 + b^2 = c^2

For this problem, we can say that a is x and b is x + 7. The hypotenuse would be x + 9

Using these terms we can write this equation and solve for x:

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

Expanding the terms gives:

x^2 + x^2 + 14x + 49 = x^2 +18x +81

Combine like terms:

2x^2 + 14x + 49 = x^2 + 18x + 81

Subtract x^2 from both sides of your equation:

2x^2 -x^2 + 14x + 49 = x^2 -x^2 +18x + 81

Then:

x^2 + 14x + 49 = 18x + 81

Subtract 18x from both sides :

x^2 + 14x -18x + 49 = 18x -18x +81

x^2 -4x +49 = 81

Subtract 81 from both sides:

x^2 -4x +49 -81 = 81-81

The result is: x^2 - 4x -32 = 0

This equation can be factored as (x-8) * (x + 4) = 0

The only positive solution is x= 8

Therefore the leg along the wall is 8, the other leg is 8+ 7 or 15. The hypotenuse would be 8 + 9 or 17.