The length of a rectangle is 12 cm. If the area of the rectangle is 72 square centimetres, what is the width (breadth) of the rectangle?

Introduction / Context:
This is a basic mensuration problem involving a rectangle. For a rectangle, the area is the product of its length and width. Here, the length and area are given, and the width must be found. It tests the ability to rearrange the area formula and perform simple division, which is very common in quantitative aptitude exams.

Given Data / Assumptions:

• Length L = 12 cm.
• Area A = 72 square centimetres.
• Formula for area of a rectangle: A = L * W, where W is width (breadth).
• We assume the rectangle has right angles and standard geometric properties.

Concept / Approach:
The approach is to use the area formula A = L * W. With A and L known, we can solve for W by dividing the area by the length. In symbols, W = A / L. This straightforward algebraic rearrangement allows us to find the unknown dimension directly. Once W is computed, we compare it with the given options to select the correct one.

Step-by-Step Solution:
Area A = L * W.Given A = 72 sq cm and L = 12 cm.So 72 = 12 * W.To find W, divide both sides by 12: W = 72 / 12.Compute 72 / 12 = 6.Therefore, width of the rectangle W = 6 cm.

Verification / Alternative check:
We can verify by recomputing the area using the found width. Take L = 12 cm and W = 6 cm. Then A = 12 * 6 = 72 sq cm, which matches the given area. This confirms that the width 6 cm is correct. Any other width would produce a different area and would not fit the given data.

Why Other Options Are Wrong:
A width of 5 cm would give area 12 * 5 = 60 sq cm, which is too small. A width of 3 cm gives area 36 sq cm, even smaller. A width of 4 cm results in area 48 sq cm, still not equal to 72. A width of 8 cm would give area 96 sq cm, which is larger than required. Therefore, only 6 cm produces the correct area of 72 sq cm.

Common Pitfalls:
Some students mix up the roles of length and width and mistakenly divide the length by the area. Others misinterpret the units, forgetting that area is measured in sq cm while length and width are in cm. Keeping the formula clear and performing the correct division ensures the right answer. Always check by multiplying the found width back with the length to see if the original area is obtained.

Final Answer:
6 cm