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A ladder 10 meters long leans against a wall. If the foot of the ladder is 6 met

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Question: A ladder 10 meters long leans against a wall. If the foot of the ladder is 6 meters away from the wall, what is the height at which the ladder touches the wall?

Options:

  1. 8 meters
  2. 6 meters
  3. 10 meters
  4. 4 meters

Correct Answer: 8 meters

Solution: 

Using Pythagorean theorem: height = √(10² - 6²) = √(100 - 36) = √64 = 8 meters.

A ladder 10 meters long leans against a wall. If the foot of the ladder is 6 met

Practice Questions

Q1
A ladder 10 meters long leans against a wall. If the foot of the ladder is 6 meters away from the wall, what is the height at which the ladder touches the wall?
  1. 8 meters
  2. 6 meters
  3. 10 meters
  4. 4 meters

Questions & Step-by-Step Solutions

A ladder 10 meters long leans against a wall. If the foot of the ladder is 6 meters away from the wall, what is the height at which the ladder touches the wall?
  • 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 (10 meters), the distance from the wall to the foot of the ladder is one side (6 meters), and the height at which the ladder touches 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: c² = a² + b².
  • Step 4: Substitute the known values into the formula: 10² = 6² + height².
  • Step 5: Calculate 10², which is 100, and 6², which is 36. So, the equation becomes: 100 = 36 + height².
  • Step 6: Rearrange the equation to find height²: height² = 100 - 36.
  • Step 7: Calculate 100 - 36, which equals 64. So, height² = 64.
  • Step 8: Take the square root of 64 to find the height: height = √64.
  • Step 9: Calculate the square root of 64, which is 8. Therefore, the height at which the ladder touches the wall is 8 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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