The length of a rectangle is 5 cm more than its breadth, and its area is 150 cm². What are its breadth and length?
Answer and explanation
Correct answer: 10 cm and 15 cm
The governing concept is the translation of a geometric word problem into a quadratic equation. Let the breadth be x cm; then the length is x + 5 cm. Since area equals length × breadth, x(x + 5) = 150, giving x² + 5x − 150 = 0. Factorising, (x − 10)(x + 15) = 0, so x = 10 or −15. A breadth cannot be negative, hence x = 10 cm and the length is 15 cm. Option A is therefore correct. Checking confirms that 10 × 15 = 150 and 15 − 10 = 5. The other options either have the wrong product or do not differ by 5 cm.
Frequently asked questions
What is the correct answer to this question?
10 cm and 15 cm
Why is this the correct answer?
The governing concept is the translation of a geometric word problem into a quadratic equation. Let the breadth be x cm; then the length is x + 5 cm. Since area equals length × breadth, x(x + 5) = 150, giving x² + 5x − 150 = 0. Factorising, (x − 10)(x + 15) = 0, so x = 10 or −15. A breadth cannot be negative, hence x = 10 cm and the length is 15 cm. Option A is therefore correct. Checking confirms that 10 × 15 = 150 and 15 − 10 = 5. The other options either have the wrong product or do not differ by 5 cm.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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