Question

A reflecting pool is shaped like a right triangle, with one leg along the wall of a building. The hypotenuse is

Answer 1

Answer:

8 ft, 15 ft, 17 ft

Step-by-step 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,

$x^2+(x+7)^2=(x+9)^2,\\ \\x^2+x^2 +14x+49=x^2+18x+81,\\ \\x^2-4x-32=0,\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144,\\ \\x_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm12}{2}=-4,\ 8.$

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