document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #154469 by Earlsdon(6294) $\"\"$ $\"About$

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Let c = the length of the hypotenuse. a and b are the other two legs.
\n" ); document.write( " $\"a+=+c-4\"$ and...
\n" ); document.write( " $\"b+=+c-2\"$ Using the Pythagorean theorem: $\"c%5E2+=+a%5E2%2Bb%5E2\"$ and making the appropriate substitutions, we get:
\n" ); document.write( " $\"c%5E2+=+%28c-4%29%5E2%2B%28c-2%29%5E2\"$ Expanding:
\n" ); document.write( " $\"c%5E2+=+%28c%5E2-8c%2B16%29%2B%28c%5E2-4c%2B4%29\"$ Simplifying:
\n" ); document.write( " $\"c%5E2+=+2c%5E2-12c%2B20\"$ Subtracting $\"c%5E2\"$ from both sides.
\n" ); document.write( " $\"c%5E2-12c%2B20+=+0\"$ Factor the trinomial.
\n" ); document.write( " $\"%28c-10%29%28c-2%29+=+0\"$ Applying the zero product rule, we have:
\n" ); document.write( " $\"c-10+=+0\"$ or $\"c-2+=+0\"$ which leads to:
\n" ); document.write( " $\"c+=+10\"$ or $\"c+=+2\"$ Discard the second solution as c, the hypotenuse cannot be smaller than either of the other two legs, so...
\n" ); document.write( " $\"highlight%28c+=+10%29\"$ m is the length of the hypotenuse.
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