SOLUTION: In a right triangle, the shortest leg is two inches less than the longer leg. The hypotenuse is two inches longer than the longer leg. Find the measures of the sides of the righ

Algebra ->  Triangles -> SOLUTION: In a right triangle, the shortest leg is two inches less than the longer leg. The hypotenuse is two inches longer than the longer leg. Find the measures of the sides of the righ      Log On


   

Question 428647: In a right triangle, the shortest leg is two inches less than the longer leg. The hypotenuse is two inches longer than the longer leg. Find the measures of the sides of the right triangle.

Answer by ewatrrr(24785) About Me  (Show Source):
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Hi

the shortest leg is two inches less than the longer leg

The hypotenuse is two inches longer than the longer leg

Let x-2, x, x+2 represent the legs and hpotenuse respectively

Applying the Pythagorean Theorem

(x-2)^2 + x^2 = (x+2)^2 

 x^2 - 4x+4 + x^2 = x^2 + 4x + 4

    x^2 - 8x = 0

  x(x-8) = 0

     x = 8in, the other leg is 6in and the hyportenuse is 10in



CHECKING our Answer***

6in^2 + 8in^2 = 36in^2 + 64in^2 = 100in^2 = 10in^2