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 Concept.
The same two facts apply: the initial right triangle, and the final flat position. Here the equation is solved using the difference of squares instead of expanding brackets.

Step 2: Key Formula or Approach.
From the right triangle: $L^2-x^2 = 25$, which factors as $(L-x)(L+x)=25$. From the sliding condition: $L-x=2$.

Step 3: Detailed Explanation.
Since $L-x=2$ and $(L-x)(L+x)=25$:
\[ 2(L+x) = 25 \Rightarrow L+x = 12.5 \]
Now solve the pair $L-x=2$ and $L+x=12.5$ together. Adding them:
\[ 2L = 14.5 \Rightarrow L = 7.25 \]
Subtracting them:
\[ 2x = 10.5 \Rightarrow x = 5.25 \]

Step 4: Final Answer.
The ladder length is $L=7.25$ m, confirming option (C).
\[ \boxed{7.25 \text{ m}} \]