SOLUTION: A right triangle has a perimeter of 36 cm and an area of 54 cm squared. What are its dimensions?

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Question 704107: A right triangle has a perimeter of 36 cm and an area of 54 cm squared. What are its dimensions?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A right triangle has a perimeter of 36 cm and an area of 54 cm squared. What are its dimensions?
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Check for integer solutions first.
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Area = a*b/2 = 54
a*b = 108
a & b = 9 and 12
c+=+sqrt%289%5E2+%2B+12%5E2%29+=+15
9 + 12 + 15 = 36
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The hard way:
a+%2B+b+%2B+sqrt%28a%5E2+%2B+b%5E2%29+=+36
ab/2 = 54
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ab = 108
b = 108/a
Sub for b
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a+%2B+108%2Fa+%2B+sqrt%28a%5E2+%2B+%28108%2Fa%29%5E2%29+=+36
a+%2B+108%2Fa+%2B+sqrt%28a%5E2+%2B+11664%2Fa%5E2%29+=+36a
a%5E2+%2B+108+%2B+sqrt%28a%5E4+%2B+11664%29+=+36a
a%5E2++-+36a+%2B+108+=+-sqrt%28a%5E4+%2B+11664%29
a%5E4+-+72a%5E3+%2B+1512a%5E2+-+7776a+%2B+11664+=+a%5E4+%2B+11664
72a%5E3+-+1512a%5E2+%2B+7776a+=+0
a = 0 (Ignore)
a%5E2+-+21a+%2B+108+=+0
(a - 9)*(a - 12) = 0
a = 9, b = 12
or vice versa