The perimeter of a rectangle is 90 cm and its breadth is 20 cm. What is the area of this rectangle in square centimetres?

Introduction / Context:
This question combines the concept of perimeter of a rectangle with the calculation of its area. Often in aptitude tests you are not directly given both length and breadth, but instead given the perimeter and one dimension. You must first deduce the missing dimension using the perimeter formula, and then use both dimensions to compute the area. This checks your ability to manipulate simple linear equations and recall basic rectangle formulas.

Given Data / Assumptions:

• The figure is a rectangle.
• Perimeter P = 90 cm.
• Breadth b = 20 cm.
• Length l is unknown and must be found.
• We are asked for the area A in square centimetres.

Concept / Approach:
The perimeter of a rectangle is given by P = 2 * (l + b). Using the known values of P and b, we can set up an equation and solve for l. Once l is known, the area is A = l * b. This is a straightforward two step process: first find the missing side from the perimeter, then find the area as a product of length and breadth.

Step-by-Step Solution:
Given P = 90 cm and b = 20 cm.Use the perimeter formula: P = 2 * (l + b).Substitute: 90 = 2 * (l + 20).Divide both sides by 2: 45 = l + 20.Solve for l: l = 45 − 20 = 25 cm.Area A = l * b = 25 * 20 = 500 sq cm.

Verification / Alternative check:
Verify that the length and breadth give the stated perimeter. With l = 25 cm and b = 20 cm, perimeter P = 2 * (25 + 20) = 2 * 45 = 90 cm, which matches the given value. This confirms that the side lengths are correct. Multiplying 25 by 20 again gives 500 sq cm, so there are no arithmetic mistakes in calculating the area.

Why Other Options Are Wrong:
Option 400 would correspond to an area with side 20 and length 20, which would give perimeter 80, not 90. Option 250 could result from multiplying 25 by 10 instead of 25 by 20. Option 450 may arise from miscalculating length as 22.5. Option 300 is also inconsistent with both the perimeter condition and the correct area formula. Only 500 sq cm satisfies all given conditions.

Common Pitfalls:
A common error is to confuse the perimeter formula with the area formula and attempt to use P = l * b. Another mistake is forgetting to divide by 2 when solving 90 = 2 * (l + 20). Some students also misread the breadth or accidentally add an extra step, such as subtracting 20 twice. Careful algebra and awareness of which formula applies help avoid these issues.

Final Answer:
The area of the rectangle is 500 sq cm.