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.