SOLUTION: The area of a right angled-triangle is 180 sq m and its perimeter is 90 m. Find the hypotenuse.

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Question 837707: The area of a right angled-triangle is 180 sq m and its perimeter is 90 m. Find the hypotenuse.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a right angled-triangle is 180 sq m and its perimeter is 90 m. Find the hypotenuse.
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Area = a*b/2 = 180
b = 360/a
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c+=+sqrt%28a%5E2+%2B+b%5E2%29+=+90+-+a+-+b
sqrt%28a%5E2+%2B+%28360%2Fa%29%5E2%29+=+90+-+a+-+360%2Fa
a%2Asqrt%28a%5E2+%2B+%28360%2Fa%29%5E2%29+=+90a+-+a%5E2+-+360
sqrt%28a%5E4+%2B+129600%29+=+90a+-+a%5E2+-+360
a%5E4+%2B+129600+=+a%5E4+-+180a%5E3+%2B+8820a%5E2+-+64800a+%2B+129600
0+=+-+180a%5E3+%2B+8820a%5E2+-+64800a
180a%5E2+-+8820a+%2B+64800+=+0
a%5E2+-+49a+%2B+360+=+0
a = 9, a = 40
--> c = 41 meters