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. Rational Numbers - Definition and Examples

    Mar 15, 23 07:45 AM

    Rational numbers
    To learn about rational numbers, write their decimal expansion, and recognize rational numbers that are repeating decimals and terminating decimals.

    Read More

  2. Area of a Trapezoid - Definition, Formula, and Examples

    Mar 13, 23 07:52 AM

    Area of a trapezoid1
    Learn how to get the area of a trapezoid using a rectangle and a triangle, the formula, and also when the height of the trapezoid is missing.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes