Length of a ladder and the Pythagorean theorem
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.
Sep 17, 23 09:46 AM
There are many ways to find the factors of 20. A simple way is to...
Jun 09, 23 12:04 PM
The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.