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