Question

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?

Answer 1

`13ft`

Explanation:

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`