Problema Solution

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 1 foot less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 3 feet.

Answer provided by our tutors

Let

h = the distance from the ground to the top of the ladder
l = the length of the ladder, l>0
d = 3 ft the distance from the bottom of the ladder to the building

The distance from the ground to the top of the ladder is 1 foot less than the length of the ladder:

h = l - 1

The ladder, the wall and the ground are sides of a right triangle.

Using the Pythagorean Theorem we have

l^2 = d^2 + h^2

plug d = 3 and h = l - 1 into the above equation:

l^2 = 3^2 + (l - 1)^2

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click here to see the equation solved for l

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l = 5 ft

The length of the ladder is 5 feet.