Squares with diagonals in the ratio 2:5\nThe diagonals of two squares are in the ratio 2:5. Find the ratio of their areas.

Introduction / Context:
Area comparisons for similar figures depend on the square of a linear scale factor. For squares, side and diagonal are linearly related, so area is proportional to the square of the diagonal as well.

Given Data / Assumptions:

• Diagonal ratio = 2 : 5
• Two perfect squares

Concept / Approach:
If a linear dimension scales by k, the area scales by k^2. Hence, Area ratio = (Diagonal ratio)^2.

Step-by-Step Solution:

Verification / Alternative check:
Let diagonals be 2d and 5d. Sides are (2d)/√2 and (5d)/√2. Their area ratio is ( (2d)^2 / 2 ) : ( (5d)^2 / 2 ) = 4d^2/2 : 25d^2/2 = 4 : 25.

Why Other Options Are Wrong:
2:25, 3:25, and 6:25 are not squares of 2:5; the correct square ratio is 4:25.

Common Pitfalls:
Using the ratio directly (2:5) instead of squaring it is a frequent error in similarity-based problems.

Final Answer:
4:25