A rectangle has a perimeter of 90 cm and a breadth of 20 cm. Using basic rectangle formulas, what is the area of this rectangle in square centimetres?

Introduction / Context:
This is a straightforward rectangle mensuration problem. The data is given via the perimeter and one side (breadth), and you are expected to derive the other side (length) and then compute area. Such questions test direct application of perimeter and area formulas for rectangles.

Given Data / Assumptions:

• Perimeter P of the rectangle = 90 cm.
• Breadth B = 20 cm.
• Length L is unknown.
• We are asked to find the area A in sq cm.

Concept / Approach:
For a rectangle: Perimeter P = 2(L + B) Area A = L * B We can rearrange the perimeter formula to find L, then multiply by B to get the area.

Step-by-Step Solution:
Given P = 90 and B = 20. Use P = 2(L + B) ⇒ 90 = 2(L + 20). Divide both sides by 2: L + 20 = 45. So L = 45 - 20 = 25 cm. Now compute area A = L * B = 25 * 20. 25 * 20 = 500 sq cm.

Verification / Alternative check:
We can recompute the perimeter using L = 25 and B = 20. Then P = 2(L + B) = 2(25 + 20) = 2 * 45 = 90 cm. This matches the given perimeter, confirming our values and the resulting area of 500 sq cm.

Why Other Options Are Wrong:
400 corresponds to a length of 20 cm (20 * 20), which would give a perimeter of 80 cm, not 90. 250 and 450 correspond to incorrect length values and do not match the given perimeter when checked.

Common Pitfalls:
A common error is to confuse half the perimeter (L + B) with a single side, or to forget to divide the perimeter by 2. Another mistake is to misread breadth as length, which might lead to incorrect subtraction. Carefully writing down the perimeter and area formulas prevents such errors.

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