Ladder Length Calculation Using Pythagorean Theorem

The problem describes a scenario that forms a right-angled triangle:

• The ladder represents the hypotenuse.
• The distance from the wall to the foot of the ladder is one leg (base).
• The height the ladder reaches on the wall is the other leg (height).

We can use the Pythagorean theorem, which states $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse.

Applying the Pythagorean Theorem

Let:

• Base ($b$) = 2.5 m
• Height ($h$) = 6 m
• Ladder Length ($L$) = ? (Hypotenuse)

According to the Pythagorean theorem:

$ L^2 = b^2 + h^2 $

Substitute the given values:

$ L^2 = (2.5 \text{ m})^2 + (6 \text{ m})^2 $

Calculate the squares:

• $ (2.5)^2 = 6.25 $
• $ (6)^2 = 36 $

Add the results:

$ L^2 = 6.25 + 36 $

$ L^2 = 42.25 $

Find the length ($L$) by taking the square root:

$ L = \sqrt{42.25} $

$ L = 6.5 \text{ m} $

Therefore, the length of the ladder is 6.5 m.