A rectangle has length 4 cm more than its breadth and area 96 cm². What is the breadth?
Answer and explanation
Correct answer: 8 cm
The governing concept is the area formula for a rectangle, A = length × breadth, combined with a quadratic equation. Let the breadth be x cm. Then the length is x + 4 cm, so the area condition becomes x(x + 4) = 96. Therefore x² + 4x − 96 = 0. Factoring gives (x + 12)(x − 8) = 0, so x = 8 or x = −12. A length cannot be negative, so the meaningful breadth is x = 8 cm. The corresponding length is 12 cm, and 8 × 12 = 96 confirms the result. Hence option B is correct. The value 6 would give area 60, 10 would give 140, and 12 would give 192 when the length is four centimetres greater, so those distractors fail the area condition.
Frequently asked questions
What is the correct answer to this question?
8 cm
Why is this the correct answer?
The governing concept is the area formula for a rectangle, A = length × breadth, combined with a quadratic equation. Let the breadth be x cm. Then the length is x + 4 cm, so the area condition becomes x(x + 4) = 96. Therefore x² + 4x − 96 = 0. Factoring gives (x + 12)(x − 8) = 0, so x = 8 or x = −12. A length cannot be negative, so the meaningful breadth is x = 8 cm. The corresponding length is 12 cm, and 8 × 12 = 96 confirms the result. Hence option B is correct. The value 6 would give area 60, 10 would give 140, and 12 would give 192 when the length is four centimetres greater, so those distractors fail the area condition.
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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