How much higher is the top of the ladder now?

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1 Answer
Apr 11, 2018

#10# feet higher

Explanation:

We know the length of the ladder and the height up the wall, so by pythagoras, we find that

#25^2 = 15^2 + G^2#

#G = 20#

Thus, the base of the ladder is #20# feet from the base of the wall. Since the length of the ladder is #25#, we see once again through pythagoras that

#(20 - 2x)^2 + (15 + x)^2 = 25^2#

#400 - 80x + 4x^2 + 225 + 30x + x^2 = 625#

#5x^2 - 50x= 0#

#x(x- 10) = 0#

#x = 0 or 10#

Since #x= 10#, the top of the ladder is #10# feet higher than at the start. However, in reality this wouldn't make too much sense because it would mean that the ladder is right up against the wall (the distance between the base and the wall would be 0 feet).

Hopefully this helps!