The length of the incline is 4 in. less than three times its height. How high is the ramp?

let h=height

let 2h+4=base

let 3h-4=incline

use the Pythagorean Theorem

h^2+(2h+4)^2=(3h-4)^2

h^2+4h^2+16h+16=9h^2-24h+16

subtract 16 from both sides

h^2+4h^2+16h=9h^2-24h

5h^2+16h=9h^2-24h

9h^2-5h^2-24h-16h=0

4h^2-40h=0

divide both sides by 4

h^2-10h=0

factor

h(h-10)=0

h-10=0

h=10 inches (the height)

the other measures are base=24 inches and incline=26 inches

this is basically a 5-12-13 right triangle with all sides doubled

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