Question

joel is designing a ramp for a bike trick. he draws this diagram like a tringle going down and base is 2x+3 and down is 2x+2 and the length is x what is the value of x

Answer 1

I need to know which side is the slanted ramp (the hypotenuse). Two interpretations:

1) If "length = x" is the hypotenuse, then by Pythagoras
(2x+3)^2 + (2x+2)^2 = x^2
=> 7x^2 + 20x + 13 = 0
=> x = -1 or x = -13/7,
so there is no positive solution (no valid ramp length).

2) If the slanted ramp (hypotenuse) is 2x+3 and the legs are x and 2x+2, then
x^2 + (2x+2)^2 = (2x+3)^2
=> x^2 + 4x^2 + 8x + 4 = 4x^2 + 12x + 9
=> x^2 - 4x - 5 = 0
=> (x-5)(x+1) = 0
so x = 5 (positive solution).

Check your diagram: if the slanted side is 2x+3 then x = 5; if the slanted side is x there is no positive solution. Which is it?