the boat launch shown is 32 meters longer than the rise of the ramp. The run is 31 meters longer than the rise. How long are the three sides of the ramp?
rise --- x m
hypotenuse -- x+32
run --- x+31
x^2 + (x+31)^2 = (x+32)^2
x^2 + x^2 + 62x + 961 = x^2 + 64x + 1024
x^2 - 2x - 63 = 0
(x-9)(x+7) = 0
x = 9, or x = -7 which would be silly
the sides are 9, 40, and 41
check:
9^2 + 40^2 = 41^2, true!
Let's denote the length of the ramp's rise as "x" meters.
According to the given information:
- The boat launch is 32 meters longer than the rise, so its length is x + 32 meters.
- The run is 31 meters longer than the rise, so its length is x + 31 meters.
Therefore, the three sides of the ramp are:
- Rise: x meters
- Run: x + 31 meters
- Boat launch: x + 32 meters
To find the lengths of the three sides of the ramp, we need to set up some equations based on the given information.
Let's say the length of the rise of the ramp is "x" meters.
According to the problem, the boat launch is 32 meters longer than the rise, so its length would be (x + 32) meters.
Similarly, the run, which is the base of the ramp, is 31 meters longer than the rise. Therefore, the length of the run would be (x + 31) meters.
So, we have the three sides of the ramp as follows:
Rise: x meters
Boat Launch: (x + 32) meters
Run: (x + 31) meters
Therefore, the lengths of the three sides of the ramp are x meters, (x + 32) meters, and (x + 31) meters.