SOLUTION: this is the problem. A right triangle has two legs with lengths a and b and a hypotenuse with length c. in this triangle, the area and perimeter are the same nonzero number. find t

Question 355054: this is the problem. A right triangle has two legs with lengths a and b and a hypotenuse with length c. in this triangle, the area and perimeter are the same nonzero number. find the length of a if b=6.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The area of the triangle is .
The perimeter, on the other hand, is . Since area = perimeter, then , or , or .
By the Pythagorean theorem,
,
,
,
,
, or
. Therefore or . Discard the first value, so . The hypotenuse is then .
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