Square diagonal scaling with doubled area: The diagonal of a square is 4√2 cm. Find the diagonal of another square whose area is double the first square’s area.

Introduction / Context:For squares, diagonal d relates to side s by d = s*sqrt(2), and area A = s^2. Doubling area scales the side by sqrt(2), which in turn scales the diagonal accordingly.

Given Data / Assumptions:

• d1 = 4*sqrt(2) cm → s1 = d1 / sqrt(2) = 4 cm
• A1 = s1^2 = 16 sq cm
• A2 = 2*A1 = 32 sq cm

Concept / Approach:If area doubles, side multiplies by sqrt(2): s2 = s1*sqrt(2). Then diagonal d2 = s2*sqrt(2) = s1*2.

Step-by-Step Solution:s2 = sqrt(32) = 4*sqrt(2)d2 = s2*sqrt(2) = 4*sqrt(2)*sqrt(2) = 8 cm

Verification / Alternative check:Diagonal scales by the same factor as side (sqrt(2)); from 4*sqrt(2) to 8 matches scaling by sqrt(2).

Why Other Options Are Wrong:8√2 cm corresponds to quadrupling area; 4√2 cm is original; 6 cm is arbitrary.

Common Pitfalls:Confusing diagonal scaling with area scaling; remember area scales with side squared.

Final Answer:8 cm