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