document.write( "Question 369221: What are the dimensions of a right triangle where the hypotenuse is 10 and the area is 20? \n" ); document.write( "

Algebra.Com's Answer #263096 by robertb(5830) $\"\"$ $\"About$

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From the given, $\"b%5E2+%2B+h%5E2+=+100\"$ , from the Pythagorean theorem. Also, $\"A+=+20+=+%281%2F2%29bh\"$ , or $\"bh+=+40\"$ , or $\"b+=+40%2Fh\"$ . By direct substitution, $\"1600%2Fh%5E2+%2B+h%5E2+=+100\"$ , or
\n" ); document.write( " $\"h%5E4-100h%5E2%2B1600+=+0\"$ ,
\n" ); document.write( " $\"%28h%5E2-80%29%28h%5E2-20%29+=+0\"$ . From this we get
\n" ); document.write( " $\"h+=+sqrt%2880%29+=+4sqrt%285%29\"$ or $\"h+=+sqrt%2820%29+=+2sqrt%285%29\"$ . For each value of h we get $\"b+=+2sqrt%285%29\"$ or $\"b+=+2sqrt%285%29\"$ respectively. Therefore there is only basically one right triangle formed, one whose leg is $\"2sqrt%285%29\"$ and the other leg $\"4sqrt%285%29\"$ .
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