A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.

To find the length of the ladder, we can use the Pythagorean theorem, as the ladder, the wall, and the ground form a right-angled triangle.

Let’s denote:
– The length of the ladder as \(L\).
– The distance of the foot of the ladder from the wall as 2.5 m.
– The height of the window above the ground as 6 m.

According to the Pythagorean theorem:

\[
L^2 = 6^2 + 2.5^2
\]

\[
L^2 = 36 + 6.25
\]

\[
L^2 = 42.25
\]

\[
L = \sqrt{42.25}
\]

\[
L = 6.5 \text{ m}
\]

Therefore, the length of the ladder is 6.5 meters.