Question

A 50-foot ladder leans against a wall so that it is 40 feet high at the top. The ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up. How much higher is the top of the ladder now?

Answer 1

Explanation:

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Answer 2

The new height of the ladder is 48 feet

How to find the new height of the ladder

Using the Pythagorean theorem, we have:

h² + d² = ladder length²

where

h = 40

d = ?

40² + d² = 50²

1600 + d² = 2500

d² = 2500 - 1600

d² = 900

d = 30

Adjusting to a new distance, 2 * 40 = 80, lets find the new height of the ladder

(30 - 2x)² + (40 + x)² = ladder length²

(30 - 2x)² + (40 + x)² = 50²

900 - 120x + 4x² + 1600 + 80x + x² = 2500

5x² - 40x + 2500 = 2500

5x² - 40x = 0

5x (x - 8) = 0

x - 8 = 0

x = 8

The new height of the top of the ladder

= 40 + x

= 40 + 8

= 48 feet