Analytic geometry easy but tricky problem

[greg_rack]

Homework Statement

The straight line with equation , y = mx + 3 where , m > 0, m ≠ 1 is perpendicular to the line with
equation y = px + 2
The lines cut the x-axis at the points L and M respectively. The length of LM is 5 units.
What is the value of m + p given that m > 1?

CARTESIAN PLANE ATTACHED BELOW

Relevant Equations

none

I started off by indicating $p=-\frac{1}{m}$ since it's perpendicular. The sum $m+p$ is now $\frac{m^2-1}{m}$.
Honestly, I can't go beyond that. The interceptions with the y-axis are of course unuseful, I tried algebraically intersecting the two lines but I came up with nothing... and I still can't get how to use that $LM=5$.

 

[DaveE]

how to use that $LM=5$.

The points L & M are on the lines when y=0. Also the distance between them is given. You can make some equations from these facts.

 

[greg_rack]

The points L & M are on the lines when y=0. Also the distance between them is given. You can make some equations from these facts.

Thanks, did it!