How to solve this word problem?

Question: A 13ft ladder is leaning against the side of a house. The distance from the house to the base of the ladder is 7 ft less than the distance from the top of the ladder to the ground. How far is the bottom of the ladder from the house?

I understand this is a triangle, and may have something to due with a theorem, and etc. I feel like it's #a^2+b^2=c^2# but I'm not sure. Can someone verify this for me? Much appreciated.

1 Answer
P dilip_k
Dec 1, 2017

Here the triangle formed by the ladder length #l=13ft# with the height of its top from the ground #h=xft# and distance of its bottom from the wall #d=(x-7)ft# is right angled one and #l# is the hypotenuse.
So by Pythagorean theorem we have

#x^2+(x-7)^2=13^2#

#=>x^2+x^2-14x+49-169=0#

#=>2x^2-14x-120=0#

#=>x^2-7x-60=0#

#=>x^2-12x+5x-60=0#

#=>x(x-12)+5(x-12)=0#

#=>(x-12)(x+5)=0#

Hence #x=12#

So distance of its bottom from the wall

#d=(12-7)ft=5ft#

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