SOLUTION: one leg of a right triangle is 14 inches longer than the smaller leg, and the hypotenuse is 16 inch longer than the smaller leg. find the lengths of the sides of the triangle

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Question 165568: one leg of a right triangle is 14 inches longer than the smaller leg, and the hypotenuse is 16 inch longer than the smaller leg. find the lengths of the sides of the triangle
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the smaller leg x
Call the hypotenuse h
The longer leg = x%2B14
h+=+x+%2B+16
h%5E2+=+x%5E2+%2B+%28x%2B14%29%5E2
%28x%2B16%29%5E2+=+x%5E2+%2B+x%5E2+%2B+28x+%2B+196
x%5E2+%2B+32x+%2B+256+=+2x%5E2+%2B+28x+%2B+196
x%5E2+-+4x+-+60+=+0
You can solve by completing the square
x%5E2+-+4x+%2B+%284%2F2%29%5E2+=+60+%2B+%284%2F2%29%5E2
x%5E2+-+4x+%2B+4+=+64
%28x+-+2%29%5E2+=+8%5E2
Take the square root of both sides
x+-+2+=+8
x+=+10
x+%2B+14+=+24
x+%2B+16+=+26
The sides are 10,24, and 26
check answer
h%5E2+=+x%5E2+%2B+%28x%2B14%29%5E2
26%5E2+=+10%5E2+%2B+24%5E2
676+=+100+%2B+576
676+=+676
OK