Rectangular plot — Length is four times breadth. A playground of 1,200 m2 occupies one-third of the total plot. Find the plot length (in meters).

Introduction / Context:Use the fraction of area to infer the total plot area, then apply the length-to-breadth ratio to determine dimensions and the required length.

Given Data / Assumptions:

• Playground area = 1,200 m2 = (1/3) of total
• Total area = 3 * 1,200 = 3,600 m2
• L = 4B

Concept / Approach:A = L * B = 4B^2 = 3,600 ⇒ B^2 = 900 ⇒ B = 30 m; then L = 4 * 30 = 120 m.

Step-by-Step Solution:B = 30 mL = 120 m

Verification / Alternative check:Area check: 120 * 30 = 3,600 ✔

Why Other Options Are Wrong:20 and 30 are breadth or distractors; 60 is half the length; “None” is false.

Common Pitfalls:Forgetting that the 1,200 m2 is only one-third of the whole plot or inverting the 4:1 ratio.

Final Answer:120