Aladder 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?

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

------> equation

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

square both sides

------> equation

Step 3

equate equation and equation

therefore

the answer is

the length of the ladder is

see the attached figure to better understand the problem

the 3rd option is right

step-by-step explanation:

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80