Rectangular plot — “Half as long again” as broad (i.e., length = 1.5 × breadth). If area is 2/3 hectares, find the length (in meters).

Introduction / Context:
Translate the phrase “half as long again” to a ratio statement and convert the given area from hectares to square meters. Then solve for breadth and compute length.

Given Data / Assumptions:

• Length L = 1.5 * breadth B
• Area = 2/3 ha = (2/3)*10,000 = 6,666.666… m2

Concept / Approach:
Area A = L * B = 1.5 * B^2 ⇒ B^2 = A / 1.5. Then length L = 1.5B.

Step-by-Step Solution:
B^2 = 6,666.666… / 1.5 = 4,444.444… ⇒ B ≈ 66.666… mL = 1.5 * 66.666… ≈ 100 m

Verification / Alternative check:
Area check: 100 * 66.666… ≈ 6,666.666… m2 ✔

Why Other Options Are Wrong:
66.66 m is the breadth, not the length; 33 m and 100/√3 m are distractors; 80 m does not satisfy the area.

Common Pitfalls:
Misinterpreting the phrase “half as long again” or forgetting hectare-to-m2 conversion.

Final Answer:
100 meters