The top of a ladder leans against a house at a height of 12 feet. The length of the ladder is 8 feet more than the distance from the house to the base of the ladder. Find the length of the ladder?

1 Answer
Mar 19, 2016

Answer:

#13ft#

Explanation:

magoosh

The ladder leans against a house at a height #AC=12 ft#
Suppose distance from the house to the base of ladder #CB=xft#
Given is that length of ladder #AB=CB+8=(x+8) ft#
From Pythagorean theorem we know that
#AB^2=AC^2+CB^2#, inserting various values
#(x+8)^2=12^2+x^2#
or #cancel(x^2)+16x+64=144+cancel(x^2)#
or #16x=144-64#
or #16x=80/16=5#
Therefore length of ladder #=5+8=13ft#

-.-.-.-.-.-.-.-.-.-.
Alternatively, one can assume length of ladder #AB=xft#
This sets the distance from the house to the base of ladder #CB=(x-8)ft#
Then proceed with setting up of equation under Pythagorean theorem and solve for #x#