During a gale a maypole was broken in such a manner that it struck the ground at a distance twenty feet from the base of the pole.

It was repaired and later broke a second time at a point five feet lower. This time it struck the ground thirty-five feet from the base.

What was the original height of the pole?

 (The first time the maypole broke)Let the portion of the pole that broke be X and the remaining portion be Y.

By Pythagoras' theorem:

Y^2 +20^2=X^2

X^2-Y^2=400

(The second time the maypole broke)

(Y-5)^2+35^2=(X+5)^2

X^2+25+10X-Y^2-25+10Y=1225

X^2+10X-Y^2+10Y-X^2+Y^2=1225-400

10X+10Y=825

X+Y=825/10=82.5

So, the length of the pole is 82.5 feet.

Posted by Sparsh on 2006-05-03 09:15:56