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A ladder is leaning against a wall. The top of the ladder is 9 feet (ft) above the ground. If the bottom of the ladder is moved 3ft farther from the wall, the ladder will be lying flat on the ground, still touching the wall. How long, in feet, is the ladder?

Verified Answer :

calculista

Step 1

First situation

when a ladder is leaning against a wall

Let

x-------> the distance of the bottom of the ladder from the wall

L-------> the length of the ladder

Find the length of the ladder

Applying the Pythagorean Theorem

\(L^{2} =x^{2}+ 9^{2}\) ------> equation \(1\)

Step 2

Second situation

when the ladder will be lying flat on the ground

Find the length of the ladder

In this situation the length of the ladder is equal to

\(L=x+3\)

square both sides

\(L^{2}=(x+3)^{2}\) ------> equation \(2\)

Step 3

equate equation \(1\) and equation \(2\)

\(x^{2}+ 9^{2}=(x+3)^{2}\\x^{2}+81=x^{2} +6x+9\\ 6x=81-9\\6x=72\\x=12\ ft\)

therefore

the answer is

the length of the ladder is \(12\ ft\)

see the attached figure to better understand the problem

View image calculista

\(3\sqrt{10} feet\sqrt{x}\) is length of the ladder.

What is Pythagoras theorem?

Pythagoras theorem defines a relation between length of sides of a right-angled triangle i.e., \({Base}^2 + {perpendicular}^2 = {Hypotenuse}^2\)

How to solve?

AB = length of ladder top from ground = 9 feet

AC = distance of ladder base from wall = 3 feet

BC = length of ladder = ?

Formula used:

\({Base}^2 + {perpendicular}^2 = {Hypotenuse}^2\)

\({AC}^2 + {AB}^2 = {BC}^2\\{3}^2 + {9}^2 = {BC}^2\)

\(\sqrt{90} feet = BC\)

Thus, the Length of the ladder is \(3\sqrt{10} feet\)

To Know more about Pythagoras theorem visit:

https://brainly.com/question/343682

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