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 length of all three sides of the reflecting pool

Answer 1

a^2 + b^2 = c^2

9^2 + 7^2 = get the answer then find the square root of it

Answer 2

Answer: The length of all three sides of the reflecting pool are 8 feet , 17 feet and 16 feet.

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`

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