A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 44 ft shorter than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 22 ft less than the length of the ladder?
Accepted Solution
A:
Answer:88 ft Step-by-step explanation: Let l = the length of the ladder and
l - 44 = the distance along the ground and
l - 22 = the height on the building
We have a right triangle, so we can apply Pythagoras' Theorem.
[tex]\begin{array}{rcl}l^{2} & = & (l - 22)^{2} + (l - 44)^{2}\\l^{2} & = & l^{2} - 44l + 484 + l^{2} - 88l + 1936\\l^{2}& = & 2l^{2} - 132l + 2420\\l^{2} - 132l + 2420 & = & 0\\\end{array}[/tex]We must find numbers that multiply to make 2420 and add to make -132.
Some trial-and-error will give you the numbers -110 and -22.
-110 × (-22) = 2420 and -110 + (-22) = -132
Then
l - 22 = 0 l - 122 = 0
l = 22 l = 110
We reject l = 22, because that would make the height of the ladder equal to zero. Height of ladder = l - 22 = 110 - 22 = 88 ft.