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.
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