Question

Rahim plans to draw a square JKLM with point O on side JK but is not successful. Why?
A: The length of OM is twice that of OL.
B: The length of OM is 4 cm.

• A. if the question can be answered using A alone but not B alone.
• B. if the question can be answered using B alone but not A alone.
• C. if the question can be answered using A and B together, but not using either A or B alone.
• D. if the question cannot be answered even using A and B together.
• E.

Hint:

In geometry DS problems, ratios + absolute measures together often determine feasibility.

Answer 1

The Correct Option is C

To understand why Rahim is unsuccessful in drawing a square JKLM with point O on side JK, we need to examine the given conditions:

1. Condition A: The length of OM is twice that of OL.
This implies: \( OM = 2 \times OL \). However, without specific lengths, we cannot determine if this condition alone maintains the integrity of a square.

2. Condition B: The length of OM is 4 cm.
This gives: \( OM = 4 \text{ cm} \). Again, without additional points or lengths, this condition alone does not verify if a square can exist.

To address whether JKLM is a square:
- A square requires all sides to be equal and angles to be \(90^\circ\).

Combining both conditions, we have:
- From A: \( OM = 2 \times OL \) and from B: \( OM = 4 \text{ cm} \) thus \( OL = 2 \text{ cm} \).

This implies for JKLM to be a square each side must be \( 4 \text{ cm}\) (as OM is a segment within that side), but with OL = 2 cm, OM cannot equal OL. Hence, neither conditions A nor B alone provide sufficient information to confirm if JKLM can be a square. However, combined, they at least define the lengths in relation but still do not satisfy square properties.

Thus, the question can be answered using A and B together, but not using either A or B alone.