SOLUTION: Seth builds a bike ramp in the shape of a right triangle. One leg is one inch shorter than the "ramp" while the other leg , the height of the ramp, is 8 in. shorter than the ramp.

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Question 1087936: Seth builds a bike ramp in the shape of a right triangle. One leg is one inch shorter than the "ramp" while the other leg , the height of the ramp, is 8 in. shorter than the ramp. What is the height of the ramp?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the ramp be +r+%7C%7C%7C+inches+long%0D%0AAnother+leg+is+%7B%7B%7B+r+-+1+ in long
The height of the ramp is +r+-+8+ in long
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Use pythagorean theorem
+%28+r+-+1+%29%5E2+%2B+%28+r+-+8+%29%5E2+=+r%5E2+
+r%5E2+-+2r+%2B+1+%2B+r%5E2+-+16r+%2B+64+=+r%5E2+
+2r%5E2+-+18r+%2B+65+=+r%5E2+
+r%5E2+-+18r+%2B+65+=+0+
complete the square:
+r%5E2+-+18r+%2B+%2818%2F2%29%5E2+=+-65+%2B+%2818%2F2%29%5E2+
+r%5E2+-+18r+%2B+81+=+-65+%2B+81+
+%28+r+-+9+%29%5E2+=+16+
+%28+r+-+9+%29%5E2+=+4%5E2+
+r+-+9+=+4+
+r+=+13+
and the other solution is:
+r+-+9+=+-4+
+r+=+5+
( I can't use this solution because I cannot subtract +8+ from it )
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+r+=+13+
+r+-+1+=+12+
+r+-+8+=+5+
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The height of the ramp is 5 in
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check answer:
+%28+r+-+1+%29%5E2+%2B+%28+r+-+8+%29%5E2+=+r%5E2+
+12%5E2+%2B+5%5E2+=+13%5E2+
+144+%2B+25+=+169+
+169+=+169+
OK