How do i find lateral height with only surface area and length of the edge?

I'm guessing you are talking about the surface area of a cone?
Also by length of the edge, do you mean slant height?
Here is the area formula for a cone:
Lateral Area = (π • r • slant height)
Solving for "r" we get:

radius = Lateral Area / (π • slant height)

When you calculate the radius, you can solve for the height by
height^2 = slant height^2 - radius^2

Your cleary not see the answer is 25

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