Rectangle — Area 144 cm^2 and Sides in Ratio 4 : 9: Find the perimeter of the rectangle.

Introduction / Context:
When area and side ratio are known, scale factor k follows from (4k)*(9k) = 144. After finding sides, compute the perimeter. This avoids solving two unknowns independently by leveraging the ratio constraint.

Given Data / Assumptions:

• Sides = 4k and 9k (cm)
• Area = 144 cm^2
• Perimeter P = 2(4k + 9k)

Concept / Approach:
Compute k^2 from area and take the positive root. Then compute perimeter directly. Keep units in centimetres consistently.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 56, 60, 64 arise from incorrect k or arithmetic.
• 48 assumes equal sides (square), which is not given.

Common Pitfalls:

• Using 4 + 9 = 13 as area; remember area uses multiplication.

Final Answer:
52 cm.