Rectangle — Ratio 5 : 3 and Length 8 m More: The ratio of length to breadth is 5 : 3, and length is 8 m more than breadth. Find the area (in square metres).

Introduction / Context:Rectangles with a given side ratio and an additive difference can be solved with a single variable. Convert the ratio to algebra, use the difference to find the scale, then compute area as length times breadth in square metres.

Given Data / Assumptions:

• L : B = 5 : 3
• L = B + 8
• Units in metres

Concept / Approach:Let L = 5k and B = 3k. Then L − B = 2k = 8 ⇒ k = 4. Substitute back to get actual dimensions and multiply to obtain area. This linear system avoids guesswork and ensures consistency.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 300 and 250 assume other k values.
• 185 and 196 do not match the derived dimensions.

Common Pitfalls:

• Mistaking which term in the ratio corresponds to length vs breadth.

Final Answer:240 sq m.