SOLUTION: The longer leg of a given right triangle is 7ft greater in length than the shorter leg of the triangle. The hypotenuse is 2ft greater in length than the longer leg of the triangle.

 

Hi,

The longer leg of a given right triangle is 7ft greater in length than the shorter leg of the triangle. 

The hypotenuse is 2ft greater in length than the longer leg of the triangle.

Using the Pythagorean Theorem

  a^2 + b^2 = c^2

 a^2 + (a+7)^2 = (a+9)^2

 a^2 + a^2 + 14a + 49 = a^2 + 18a + 81

    a^2 - 4a - 32 = 0

factoring

 (a -8)(a + 4) = 0

 (a + 4) = 0 ,  a = -4  ||disregard negative solution for unit measure

0r (a - 8)= 0 , a = 8ft,  b = 15ft,  c = 17ft

and...