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

17, 8 , 15

Explanation:

Answer 2

8 ft, 15 ft, 17 ft

Explanation:

Let x feet be the length of the side along the building. If the hypotenuse is 9 feet longer than the side along the building, then the length of the hypotenuse is x+9 feet. If the third side is 7 feet longer than the side along the building, then the length of the third side is x+7 feet.

This triangle is right triangle. By the Pythagorean theorem,

`x^2+(x+7)^2=(x+9)^2,\\ \\x^2+x^2 +14x+49=x^2+18x+81,\\ \\x^2-4x-32=0,\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144,\\ \\x_(1,2)=(-(-4)\pm√(144))/(2\cdot 1)=(4\pm12)/(2)=-4,\ 8.`

The length of the side cannot be negative, thus x=8 ft. Then x+7=15 ft, x+9=17 ft.