Problema Solution
A ladder of length 2x+1 feet is positioned against a wall such that the bottom is x-1 feet away from a wall. The distance between the floor and the top of the ladder is 2xfeet.
Find the length of the ladder.
The length of the ladder is ____feet.
Assume that a right angle is formed by the wall and the floor.
Answer provided by our tutors
The ladder forms a right-angled triangle.
So,
(2x)^2 + (x-1)^2 = (2x+1)^2
or, 4x^2 + x^2 +1 - 2x= 4x^2 +1+4x
or, 5x^2 + 1 - 2x =4x^2 + 1 + 4x
or, x^2 - 6x = 0
x= 0 or 6
Length of ladder = 2x+1 = 13 feet