SOLUTION: One leg of a right triangle is 4 m less than the hypotenuse. The other leg is 2 m less than the hypotenuse. Find the length of the hypotenuse.

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Question 204677: One leg of a right triangle is 4 m less than the hypotenuse. The other leg is 2 m less than the hypotenuse. Find the length of the hypotenuse.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let c = the length of the hypotenuse. a and b are the other two legs.
a+=+c-4 and...
b+=+c-2 Using the Pythagorean theorem: c%5E2+=+a%5E2%2Bb%5E2 and making the appropriate substitutions, we get:
c%5E2+=+%28c-4%29%5E2%2B%28c-2%29%5E2 Expanding:
c%5E2+=+%28c%5E2-8c%2B16%29%2B%28c%5E2-4c%2B4%29 Simplifying:
c%5E2+=+2c%5E2-12c%2B20 Subtracting c%5E2 from both sides.
c%5E2-12c%2B20+=+0 Factor the trinomial.
%28c-10%29%28c-2%29+=+0 Applying the zero product rule, we have:
c-10+=+0 or c-2+=+0 which leads to:
c+=+10 or c+=+2 Discard the second solution as c, the hypotenuse cannot be smaller than either of the other two legs, so...
highlight%28c+=+10%29m is the length of the hypotenuse.