Hi,

The hypotenuse of a triangle is 5 feet long

the longer of the two legs is one foot longer than the shorter 

Applying the Pythagorean Theorem:  legs  and 

 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 

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