boating
The inclined ramp of a boat launch is 8 meters longer than the rise of the ramp.
The run is 7 meters longer than the rise. How long are the three sides of the ramp?
let the the rise be x m
then the run is x+7 m , and the ramp (the hypotenuse) is x+8 m
then
x^2 + (x+7)^2 = (x+8)^2
expand and simplify to
x^2 - 2x - 15=0
x^2 - 2x - 15=0
(x-5)(x+3)=0
x = 5 or x =-3
clearly x has to be positive
so the height of the ramp is 5,
would the other sides be
13m and 12m?
correct.
thank you
To find out the lengths of the other two sides of the ramp, we'll substitute the value of x = 5 into the expressions for the run and the ramp.
The run (x+7) becomes 5 + 7 = 12 m.
The ramp (x+8) becomes 5 + 8 = 13 m.
Therefore, the lengths of the three sides of the ramp are: rise = 5 m, run = 12 m, and ramp = 13 m.