Rectangle with Diagonal — One side is 4 m and the diagonal is 5 m. Find the area of the rectangle.

Introduction / Context:
Use the Pythagorean relation between sides and diagonal to find the missing side, then multiply for area.

Given Data / Assumptions:

• One side = 4 m
• Diagonal = 5 m

Concept / Approach:
If sides are a and b, and diagonal d, then d^2 = a^2 + b^2. Here a = 4, d = 5, so b = sqrt(d^2 − a^2) = sqrt(25 − 16) = 3. Area = a * b.

Step-by-Step Solution:
b = 3 mArea = 4 * 3 = 12 m2

Verification / Alternative check:
Classic 3-4-5 right triangle confirms correctness.

Why Other Options Are Wrong:
15, 20 m2 mismatch area; 4√5 m2 is not area here; 9 m2 is 3*3, not applicable.

Common Pitfalls:
Using perimeter or misapplying diagonal formula.

Final Answer:
12 m2