Catenaries on "Car Talk"

Here's a puzzle from the radio show, Car Talk, with the misspelling corrected:

"There are two telephone poles. Each one is 100-feet tall. They are parallel and an unknown distance apart.

"We're going to attach a 150-foot rope from the very top of one of the poles to the top of the other. This rope will, of course, droop down somewhat. That drooping rope is called a catenary, from the Latin word for chain.

"The question is: What must be the distance between the two poles, so that the lowest point of the catenary is 25-feet above the ground?"

I confess, I worked out the equation for a catenary to try to answer this, but that's a waste of time if you think about the problem a little.

The answer, if you need it, is here.