SOLUTION: What are the dimensions of a right triangle where the hypotenuse is 10 and the area is 20?

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Question 369221: What are the dimensions of a right triangle where the hypotenuse is 10 and the area is 20?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
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
h%5E4-100h%5E2%2B1600+=+0,
%28h%5E2-80%29%28h%5E2-20%29+=+0. From this we get
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 .