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Valerie makes a bike ramp in the shape of a right triangle. The base of the ramp is 4 in. more than twice its height, look below for more details

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

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Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (7 lesson ratings) (7)
2
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
Amarjeet K. | Professional Engineer for Math and Science TuroringProfessional Engineer for Math and Scien...
4.6 4.6 (8 lesson ratings) (8)
-2

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