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A ladder is leaning against a wall. If the foot of the ladder is 6 meters away f

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Question: A ladder is leaning against a wall. If the foot of the ladder is 6 meters away from the wall and the top of the ladder reaches a height of 8 meters on the wall, what is the length of the ladder?

Options:

  1. 10 meters
  2. 12 meters
  3. 14 meters
  4. 16 meters

Correct Answer: 10 meters

Solution: 

Using the Pythagorean theorem, length of ladder = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 meters.

A ladder is leaning against a wall. If the foot of the ladder is 6 meters away f

Practice Questions

Q1
A ladder is leaning against a wall. If the foot of the ladder is 6 meters away from the wall and the top of the ladder reaches a height of 8 meters on the wall, what is the length of the ladder?
  1. 10 meters
  2. 12 meters
  3. 14 meters
  4. 16 meters

Questions & Step-by-Step Solutions

A ladder is leaning against a wall. If the foot of the ladder is 6 meters away from the wall and the top of the ladder reaches a height of 8 meters on the wall, what is the length of the ladder?
  • Step 1: Identify the problem. We have a ladder leaning against a wall, forming a right triangle with the wall and the ground.
  • Step 2: Label the sides of the triangle. The distance from the wall to the foot of the ladder is 6 meters (this is one side), and the height the ladder reaches on the wall is 8 meters (this is the other side).
  • Step 3: Use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides.
  • Step 4: Write the formula. The formula is: length of ladder (hypotenuse) = √(distance from wall^2 + height on wall^2).
  • Step 5: Plug in the values. We have distance from wall = 6 meters and height on wall = 8 meters. So, we calculate: length of ladder = √(6^2 + 8^2).
  • Step 6: Calculate the squares. 6^2 = 36 and 8^2 = 64.
  • Step 7: Add the squares together. 36 + 64 = 100.
  • Step 8: Take the square root of the sum. √100 = 10.
  • Step 9: State the final answer. The length of the ladder is 10 meters.
  • Pythagorean Theorem – A mathematical principle used to find the length of a side in a right triangle, stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
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