A rectangle has a perimeter of 48 cm and a breadth of 10 cm. Using the formulae for perimeter and area, what is the area of this rectangle in square centimetres?

Introduction / Context:
This is another basic rectangle problem, similar in style to many aptitude questions. You are given the perimeter and one side (the breadth) and must determine the area. This tests both your formula knowledge and your algebraic manipulation skills.

Given Data / Assumptions:

• Perimeter P = 48 cm.
• Breadth B = 10 cm.
• Length L is unknown.
• We must find the area A = L * B in sq cm.

Concept / Approach:
The perimeter P of a rectangle is: P = 2(L + B) From this, we can solve for L: L + B = P / 2 ⇒ L = (P / 2) − B Once we have L, we use: A = L * B

Step-by-Step Solution:
Given P = 48 and B = 10. Compute P / 2: 48 / 2 = 24. So L + B = 24 ⇒ L = 24 − 10 = 14 cm. Now compute the area: A = L * B = 14 * 10. Thus A = 140 square centimetres.

Verification / Alternative check:
Check the perimeter with L = 14 and B = 10: P = 2(L + B) = 2(14 + 10) = 2 * 24 = 48 cm, which matches the given perimeter. Therefore the dimensions 14 cm by 10 cm are correct, and the product 140 is indeed the area.

Why Other Options Are Wrong:
240 would correspond to a length of 24 cm, giving perimeter 2(24 + 10) = 68 cm, not 48. 480 and 440 are much too large and represent miscalculations like multiplying perimeter by a side or adding values incorrectly.

Common Pitfalls:
Learners sometimes forget to divide the perimeter by 2 first or inadvertently use a square formula (like side²) as if the rectangle were a square. Writing down the formulas and solving them step by step helps avoid these mistakes.

Final Answer:
The area of the rectangle is 140 sq cm.