Question
Download Solution PDFA ladder leans against a vertical wall. The top of the ladder is 8 metres above the ground. When the bottom of the ladder is moved 2 metres farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The top of the ladder is 8 metres above the ground, and the bottom is initially at a certain distance from the wall.
When the bottom is moved 2 metres farther, the ladder reaches the foot of the wall.
Formula used:
Using the Pythagorean theorem:
If the length of the ladder is L, the initial distance from the wall is x, and the height is 8 metres:
L2 = x2 + 82
After moving the bottom 2 metres farther:
L2 = (x + 2)2
Calculation:
From the first equation:
L2 = x2 + 64
From the second equation:
L2 = (x + 2)2
Equating both:
x2 + 64 = x2 + 4x + 4
⇒ 64 = 4x + 4
⇒ 60 = 4x
⇒ x = 15 metres
Substituting x = 15 into the first equation:
L2 = 152 + 64
⇒ L2 = 225 + 64
⇒ L2 = 289
⇒ L = √289
⇒ L = 17 metres
∴ The length of the ladder is 17 metres.
Last updated on May 10, 2025
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