A ladder 25 feet long is leaning against a wall such that it touches 24 feet high window. How far is the foot of the ladder from the wall?
- 24.5 feet
- 12 feet
- 9 feet
- 7 feet
The Correct Option is D
Solution and Explanation
| Concept | Using the Pythagorean theorem to find the distance from the foot of the ladder to the wall. |
|---|---|
| Given | Ladder length (hypotenuse) = 25 feet, height up the wall = 24 feet |
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
c2=a2+b2
Here, c = 25 feet and b = 24 feet. Let a be the distance from the foot of the ladder to the wall. We need to find a:
252=a2+242
Calculate 252 and 242:
252=625
242=576
Substitute these values back into the equation:
625=a2+576
Rearrange to solve for a2:
a2=625-576
a2=49
Take the square root of both sides to find a:
a=49=7
Therefore, the foot of the ladder is 7 feet from the wall.
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