Length of a ladder and the Pythagorean theorem

by Anonymous

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 18 ft. Find the length of the ladder if the length is 6 ft more than its distance from the wall.

Let d be the distance from the wall, then d + 6 is the length of the ladder as shown in the picture above.

Using the Pythagorean theorem, we get:

(d + 6)2 = d2 + 182

d2 + 12d + 36 = d2 + 182

12d + 36 = 324

12d = 324 - 36

12d = 288

d = 288/12

d = 24

Since d + 6 = 24 + 6 = 30, the length of the ladder is 30.

Click here to post comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Geometry word problems.

Recent Articles

  1. Probability Line - Definition and Examples

    Nov 21, 19 02:38 PM

    What is a probability line ? Things that you must know before doing problems ...

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

                                 Follow me on Pinterest

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.