The perimeter of a rectangle is 68 cm, and its diagonal measures 26 cm. What is the area of the rectangle?

Question

The perimeter of a rectangle is 68 cm, and its diagonal measures 26 cm. What is the area of the rectangle?

1. A. 480
2. B. 676
3. C. 240 (Correct answer)
4. D. 560

Correct Answer

Option C — 240

Detailed Solution & Explanation

The correct answer is 240.

Key Points

• Perimeter 68 cm gives 2(l + w) = 68, so l + w = 34.
• The diagonal is 26 cm, so by Pythagoras l² + w² = 676.
• Square the first relation: (l + w)² = 1156, i.e. l² + w² + 2lw = 1156.
• Substitute: 676 + 2lw = 1156 → 2lw = 480 → lw = 240.
• The area is lw = 240 cm².

Additional Information

• The individual sides are never needed, though solving gives 24 cm and 10 cm — which indeed satisfy 24 + 10 = 34 and 24² + 10² = 676.
• The identity (l + w)² = l² + w² + 2lw is the standard bridge between perimeter and diagonal data.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*