Question 618436
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Hi,
The hypotenuse of a triangle is 5 feet long
the longer of the two legs is one foot longer than the shorter {{{x}}}
Applying the Pythagorean Theorem:  legs {{{x}}} and {{{x+1}}}
 x^2 + (x+1)^2 = 25
 x^2 + x^2 + 2x + 1 = 25
 2x^2 + 2x - 24 = 0
  x^2+x-12 = 0
factoring
 (x + 4)(x-3) = 0
  x = 3  throwing out negative solution for unit of measure
  x = 3ft, the shorter leg.  The longer leg is 4ft
 AND
 3^2 + 4^2 = 5^3