Question

A ladder is lying against a wall which is 5 metres high. If the ladder slips 2 metres away from the wall, the top of the ladder touches the foot of the wall. The length of the ladder is

• A. 5 m
• B. 5.25 m
• C. 7.25 m
• D. 4 m

Hint:

Use the right triangle formed initially (wall, ground, ladder), then note the ladder's final length equals the new base distance once it lies flat.

Answer 1

The Correct Option is C

Step 1: Understanding the Question.
A ladder leans against a wall that is 5 metres high, with its top exactly at the top of the wall, and its base a distance \(x\) metres from the wall. When the base slides 2 metres further away, the top of the ladder ends up level with the ground at the foot of the wall, so the ladder now lies flat, stretching from the wall's base to the ladder's new foot. We need the ladder's length \(L\).

Step 2: Key Formula or Approach.
In the first position, the wall, the ground and the ladder form a right triangle, so by the Pythagoras theorem:
\[ L^2 = x^2+5^2 \]
In the second position, both ends of the ladder touch the ground, so the ladder's length equals the new base distance:
\[ L = x+2 \]

Step 3: Detailed Explanation.
Substitute \(L=x+2\) into \(L^2=x^2+25\):
\[ (x+2)^2=x^2+25 \]
Expand the left side:
\[ x^2+4x+4=x^2+25 \]
Cancel \(x^2\) from both sides:
\[ 4x+4=25 \]
\[ 4x=21 \Rightarrow x=5.25 \]

Step 4: Final Answer.
\[ L=x+2=5.25+2=7.25 \text{ m} \]
Options (A) 5 m and (B) 5.25 m are actually the value of \(x\), not \(L\), so they are common mistakes rather than the answer.
\[ \boxed{7.25 \text{ m}} \]