A 36 cm long thread is used to wrap a rectangular book such that the thread goes twice around the length and once around the breadth of the book. What is the area of the face of the book in square centimetres?

Introduction / Context:
This question is a classic perimeter based problem where a thread wraps around the sides of a rectangle in a specific pattern. From the total length of the thread and the wrapping pattern, you must derive equations for the length and breadth, and then compute the area of the rectangular face of the book.

Given Data / Assumptions:

• Total length of thread = 36 cm
• Thread goes twice around the length and once around the breadth
• Let length of book = L cm
• Let breadth of book = B cm
• The thread path is 2L + B, assuming a single loop pattern along one face

Concept / Approach:
The key idea is to interpret the phrase “twice around the length and once around the breadth” as indicating that the total thread length is equal to 2L + B. This gives one linear equation in L and B. Since we are asked for area, and several combinations of L and B can satisfy the same 2L + B value, we identify which combination leads to one of the given answer options for area. This is a typical multiple choice strategy question.

Step-by-Step Solution:
From the wording, total thread length = 2L + B Given 2L + B = 36 We look for integer pairs (L, B) that satisfy this and yield an area matching one of the options Try L = 6, then 2*6 + B = 36 ⇒ 12 + B = 36 ⇒ B = 24 Area = L * B = 6 * 24 = 144 sq.cm 144 sq.cm appears in the options and is a reasonable book face area Thus we take area = 144 sq.cm

Verification / Alternative check:
Another possible solution is L = 12, B = 12 (2*12 + 12 = 36) giving area 144 sq.cm again. This shows that although length and breadth may vary while satisfying the same loop condition, the area 144 sq.cm remains compatible with the given options, and therefore is the valid choice.

Why Other Options Are Wrong:
288 sq.cm, 188 sq.cm, 244 sq.cm, 196 sq.cm: None of these areas arise from integer length and breadth pairs that satisfy 2L + B = 36 in a natural book sized range, and they do not match the consistent pattern found for 144 sq.cm.

Common Pitfalls:
Misinterpreting the wrapping pattern as 2(L + B) instead of 2L + B. Trying to find unique L and B rather than focusing on area that matches the options. Arithmetic errors while testing pairs of L and B.

Final Answer:
The area of the face of the book is 144 sq.cm