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 2x feet.
Find the length, in feet, of the ladder
Answer provided by our tutors
the ladder, the floor and the wall make a right triangle
using the Pythagorean Theorem we can write
(2x+1)^2 = (x-1)^2 + (2x)^2
by solving the equation we find
x1 = 0
x2 = 6
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x1 = 0 is not a solution because we will have x-1 = 0-1 = -1 <0
for x = 6 we have
2*6 + 1 = 13 ft
the length of the ladder is 13 feet.