A rectangle has perimeter 50 cm and area 150 cm². What are its length and breadth?
Answer and explanation
Correct answer: 10 cm and 15 cm
The governing relations are perimeter = 2(l + b) and area = lb. From 2(l + b) = 50, we obtain l + b = 25, while the area condition gives lb = 150. Let either dimension be t; then the two dimensions are roots of t² − 25t + 150 = 0. Factoring gives (t − 10)(t − 15) = 0, so the dimensions are 10 cm and 15 cm. Option A is correct. Verification is important: 2(10 + 15) = 50 cm and 10 × 15 = 150 cm². Option B has the correct perimeter but area 144, option C has area 156, and option D has area 136, so none of them satisfies both conditions.
Frequently asked questions
What is the correct answer to this question?
10 cm and 15 cm
Why is this the correct answer?
The governing relations are perimeter = 2(l + b) and area = lb. From 2(l + b) = 50, we obtain l + b = 25, while the area condition gives lb = 150. Let either dimension be t; then the two dimensions are roots of t² − 25t + 150 = 0. Factoring gives (t − 10)(t − 15) = 0, so the dimensions are 10 cm and 15 cm. Option A is correct. Verification is important: 2(10 + 15) = 50 cm and 10 × 15 = 150 cm². Option B has the correct perimeter but area 144, option C has area 156, and option D has area 136, so none of them satisfies both conditions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
