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A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 met

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Question: A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 meters away from the wall, how high does the ladder reach on the wall?

Options:

  1. 24 meters
  2. 20 meters
  3. 21 meters
  4. 22 meters

Correct Answer: 20 meters

Solution: 

Using Pythagoras: height = √(25^2 - 7^2) = √(625 - 49) = √576 = 24 meters

A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 met

Practice Questions

Q1
A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 meters away from the wall, how high does the ladder reach on the wall?
  1. 24 meters
  2. 20 meters
  3. 21 meters
  4. 22 meters

Questions & Step-by-Step Solutions

A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 meters away from the wall, how high does the ladder reach on the wall?
Correct Answer: 24 meters
  • Step 1: Understand that the ladder, the wall, and the ground form a right triangle.
  • Step 2: Identify the lengths of the sides of the triangle. The ladder is the hypotenuse (25 meters), the distance from the wall to the foot of the ladder is one side (7 meters), and the height the ladder reaches on the wall is the other side (unknown).
  • Step 3: Use the Pythagorean theorem, which 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). The formula is: c^2 = a^2 + b^2.
  • Step 4: In our case, let c = 25 meters (the ladder), a = 7 meters (the distance from the wall), and b = the height we want to find.
  • Step 5: Rearrange the formula to find b: b^2 = c^2 - a^2.
  • Step 6: Substitute the values into the formula: b^2 = 25^2 - 7^2.
  • Step 7: Calculate 25^2, which is 625, and 7^2, which is 49.
  • Step 8: Subtract 49 from 625: 625 - 49 = 576.
  • Step 9: Take the square root of 576 to find b: √576 = 24.
  • Step 10: Conclude that the height the ladder reaches on the wall is 24 meters.
  • Pythagorean Theorem – The relationship between the lengths of the sides of a right triangle, where the square of the hypotenuse is equal to the sum of the squares of the other two sides.
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