SOLUTION: The inclined ramp used for loading cars in a truck is 8m longer than the rise. The run is 7m longer than the rise. How long are the 3 sides of the ramp?
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Question 1088108: The inclined ramp used for loading cars in a truck is 8m longer than the rise. The run is 7m longer than the rise. How long are the 3 sides of the ramp? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! the inclined ramp use for loading cars in a truck is 8m longer than the rise of the ramp.
The run is 7m longer than the rise. How long are the three sides of the ramp
:
let r = the rise of the ramp
then
(r+8) = length of the ramp
and
(r+7) = the horizontal run of the ramp
:
We can use pythagorus
r^2 + (r+7)^2 = (r+8)^2
FOIL (r+7)(r+7) and (r+8)(r+8)
r^2 + r^2 + 14r + 49 = r^2 + 16r + 64
Combine like terms on the left
r^2 + r^2 - r^2 + 14r - 16r + 49 - 64 = 0
r^2 - 2r - 15 = 0
You can use the quadratic formula a=1; b=-2, c=-15, but this will factors to:
(r-5)(r+3) = 0
the positive solution is all we want here
r = 5 ft
then
5 + 8 = 13 ft is the length of the ramp
and
5 + 7 = 12 ft is the horizontal run of the ramp
:
:
See if that checks out
5^2 + 12^2 = 13^2
25 + 144 = 169
