Equal areas: circle vs square — compare diameter and diagonal:\nIf a circle and a square have equal areas, what is (diameter of circle / diagonal of square)^2?

Introduction / Context:
Equate the areas to relate the circle radius to the square side. Then express the requested squared ratio in those terms. Using π = 22/7 gives a clean rational result matching options.

Given Data / Assumptions:

• Area(circle) = Area(square).
• Let circle radius = r, square side = s.
• Use π = 22/7 for final numeric comparison to options.

Concept / Approach:
πr^2 = s^2 ⇒ (diameter/diagonal)^2 = (2r / (s√2))^2 = (4r^2)/(2s^2) = 2r^2/s^2 = 2/π.

Step-by-Step Solution:

Verification / Alternative check:
Direct substitution with any r (e.g., r = 1) produces the same 2/π expression; rationalizing with 22/7 yields 7/11.

Why Other Options Are Wrong:
11/7 and 9/7 invert the correct value; 7/9 mismatches; 2/π is the unsimplified exact form but the keyed answer is its 22/7 evaluation.

Common Pitfalls:
Comparing diameter to side (not diagonal), or forgetting the √2 for the square’s diagonal.

Final Answer:
7/11