Asked by mary
the boat launch shown is 32 meters longer than the rise of the ramp. The run is 31 meters longer than the rise. How long are the three sides of the ramp?
Answers
Answered by
Reiny
rise --- x m
hypotenuse -- x+32
run --- x+31
x^2 + (x+31)^2 = (x+32)^2
x^2 + x^2 + 62x + 961 = x^2 + 64x + 1024
x^2 - 2x - 63 = 0
(x-9)(x+7) = 0
x = 9, or x = -7 which would be silly
the sides are 9, 40, and 41
check:
9^2 + 40^2 = 41^2, true!
hypotenuse -- x+32
run --- x+31
x^2 + (x+31)^2 = (x+32)^2
x^2 + x^2 + 62x + 961 = x^2 + 64x + 1024
x^2 - 2x - 63 = 0
(x-9)(x+7) = 0
x = 9, or x = -7 which would be silly
the sides are 9, 40, and 41
check:
9^2 + 40^2 = 41^2, true!
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