SOLUTION: hi. if my hypotenuse is 600, and the perimeter of the entire triangle is 1400, how long is the two other sides?

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Question 390664: hi. if my hypotenuse is 600, and the perimeter of the entire triangle is 1400, how long is the two other sides?

Answer by robertb(4012) About Me  (Show Source):
You can put this solution on YOUR website!
From the Pythagorean theorem, x%5E2+%2B+y%5E2+=+360000.
From the perimeter condition, x + y + 600 = 1400, or y = 800 - x.
Substitute this into the 1st equation, to get
x%5E2+%2B+%28800+-+x%29%5E2+=+360000,
<==> 2x%5E2+-+1600x+%2B+280000+=+0,
<==> x%5E2+-+800x+%2B+140000+=+0.
Using the quadratic formula, we get
x+=+%28800+%2B-+200sqrt%282%29%29%2F2+=+400+%2B-+100sqrt%282%29+.
If x+=+400+%2B+100sqrt%282%29, then y+=+400+-+100sqrt%282%29.
If x+=+400+-+100sqrt%282%29, then y+=+400+%2B+100sqrt%282%29.
Hence there is only 1 pair of values for the legs, and those are +400+-+100sqrt%282%29 and 400+%2B+100sqrt%282%29.