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?
please explain how to do this one
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
Can you take it from there?
(it factors)
is this right
x^2 -2x-15=0
x^2-1x-1x-15=0
-1x(-1x+1) -1(-1x+1)
is this right?
no
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, take it from there.
ok
so if the height is 5 then other side would be
13m and 12m?
To solve this problem, we need to analyze the given information and use that to determine the lengths of the three sides of the ramp.
Let's assign variables to the lengths of the three sides:
- Rise of the ramp: x meters
- Inclined ramp: x + 8 meters
- Run of the ramp: x + 7 meters
According to the given information, the inclined ramp is 8 meters longer than the rise and the run is 7 meters longer than the rise. This can be expressed mathematically as:
- Inclined ramp = Rise + 8
- Run = Rise + 7
We can now set up two equations based on the above information:
1. x + 8 = x + 7 (equating the inclined ramp and run to their respective lengths in terms of the rise)
2. x = Rise
For equation 1, we can solve it to find the value of x (the rise). Simplifying the equation, we have:
x + 8 = x + 7
x - x = 7 - 8
0 = -1
Since 0 does not equal -1, this equation has no solution. This means that the given problem is not solvable as stated.
Please note that there may be additional information missing or there could be an error in the problem statement.