Question: math answers for word problems? View Single Post
 jcaron2 Posts: 983, Reputation: 1034 Senior Member #2 Sep 7, 2011, 09:18 PM
The base of the ladder is 9' from the building, while the fence is 3' from it. Hence, the base of the ladder is 6' from the fence. In that 6' distance, the ladder has to go up at least 9' to get over the fence. Hence it has a slope of at least 9/6 = 1.5 (i.e. The ladder goes up 1.5' for every 1' of distance it covers over the ground). In all the ladder covers 9' of ground between its base and the side of the house. At a slope of 1.5, the top of the ladder would therefore be 13.5' above the ground. (Another way to look at this would be that the ladder passes over the top of the fence 9' off the ground with a slope of 1.5' of rise for every 1' of run. Thus in the remaining 3' between the fence and the house, the ladder would go up an additional 4.5' for a total height of 13.5'). I would think a ladder 13.5' in the air would be high enough to wash a 14' window.

Now to find the required length of the ladder you need to use the Pythagorean theorem:

$L^2=9^2+13.5^2$

$L=\sqrt{263.25}$

$L \approx 16.2$ feet.

Does that make sense?