Square area 1024 sq cm → rectangle dimensions from square side:\nA square has area 1024 sq cm. Consider a rectangle whose length is twice the square’s side and whose breadth is 12 cm less than that side. Find the ratio length : breadth of the rectangle.

Introduction / Context:
Use the square’s area to get its side, then translate to the rectangle’s dimensions and simplify the ratio.

Given Data / Assumptions:

• Square area = 1024 ⇒ side s = √1024 = 32 cm.
• Rectangle: length L = 2s = 64 cm; breadth B = s − 12 = 20 cm.

Concept / Approach:
Compute L:B and reduce to lowest terms.

Step-by-Step Solution:

Verification / Alternative check:
Values are integers and consistent with the description.

Why Other Options Are Wrong:
14:9, 13:12, 17:13 do not match 64:20.

Common Pitfalls:
Mistaking “twice the side” as “side + 2”.

Final Answer:
16:5.