Question 668419
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Hi,
The longer leg{{{highlight(b)}}} of a given right triangle is 7ft greater in length than the shorter leg{{{highlight(a)}}} of the triangle. 
The hypotenuse{{{highlight(c)}}} is 2ft greater in length than the longer leg{{{highlight(b)}}} 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...
{{{64 + 225 = 289}}}