Answer: The length of all three sides of the reflecting pool are 8 feet , 17 feet and 16 feet.
Step-by-step explanation:
Let sides along the building be 'x', then the measure of hypotenuse = x+9 and the measure of third side = 7+x
Since , the reflecting pool is shaped like a right triangle.
Then , by using Pythagoras theorem , we have
![(x+9)^2=x^2+(x+7)^2\\\\\Rightarrow\ x^2+81+18x=x^2+x^2+49+14x\ \ [\text{Using }(a+b)^2=a^2+b^2+2ab ]]\\\\\Rightarrow\ x^2+81+18x=2x^2+49+14x\\\\\Rightarrow\ x^2-4x-32=0\\\\\Rightarrow\ x^2-8x+4x-32=0\\\\\Rigtarrow\ x(x-8)+4(x-8)=(x-8)(x+4)\\\\\Rightarrow\ x=8\ or -4](https://tex.z-dn.net/?f=%28x%2B9%29%5E2%3Dx%5E2%2B%28x%2B7%29%5E2%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2%2B81%2B18x%3Dx%5E2%2Bx%5E2%2B49%2B14x%5C%20%5C%20%5B%5Ctext%7BUsing%20%7D%28a%2Bb%29%5E2%3Da%5E2%2Bb%5E2%2B2ab%20%5D%5D%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2%2B81%2B18x%3D2x%5E2%2B49%2B14x%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2-4x-32%3D0%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2-8x%2B4x-32%3D0%5C%5C%5C%5C%5CRigtarrow%5C%20x%28x-8%29%2B4%28x-8%29%3D%28x-8%29%28x%2B4%29%5C%5C%5C%5C%5CRightarrow%5C%20x%3D8%5C%20or%20-4)
But length cannot be negative , it means x= 8
Now, the length of side along building = 8 feet
Length of hypotenuse = 9+8 =17 feet
Length of third side = 8+7= 16 feet