Rectangle — Area 3584 m^2 and Sides in Ratio 7 : 2: Find the perimeter of the rectangle (in metres).

Introduction / Context:
This is a scale-factor problem: area fixes k^2 when sides are in a given ratio. After computing k, sides follow, and the perimeter is twice the sum. Carry exact integers to avoid rounding in the final perimeter value.

Given Data / Assumptions:

• Sides = 7k and 2k (metres)
• Area = 3584 m^2 ⇒ (7k)(2k) = 14k^2
• Perimeter P = 2(7k + 2k)

Concept / Approach:
Solve 14k^2 = 3584 ⇒ k^2 = 256 ⇒ k = 16. Then compute sides and the perimeter. All numbers are integral, giving an exact perimeter.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 246, 286, 292 are near misses from arithmetic errors.
• 274 is unsupported by the derived dimensions.

Common Pitfalls:

• Treating 7 : 2 as a sum instead of a product when using area.

Final Answer:
288 m.