A rectangular classroom has length 8 m more than its breadth and area 240 m². What is its breadth?
Answer and explanation
Correct answer: 12 m
Apply the rectangle area formula A = length × breadth. Let the breadth be x metres. The length is then x + 8 metres, so x(x + 8) = 240. This gives x² + 8x − 240 = 0. Factoring yields (x + 20)(x − 12) = 0, with solutions x = −20 and x = 12. Since a classroom dimension cannot be negative, the breadth is 12 m. Its length is 20 m, and the check 12 × 20 = 240 confirms both the equation and the units. Therefore option B is correct. The value 20 is the length, not the breadth. Values 10 and 15 would give lengths 18 and 23 respectively, producing areas 180 m² and 345 m², so they do not satisfy the stated area condition.
Frequently asked questions
What is the correct answer to this question?
12 m
Why is this the correct answer?
Apply the rectangle area formula A = length × breadth. Let the breadth be x metres. The length is then x + 8 metres, so x(x + 8) = 240. This gives x² + 8x − 240 = 0. Factoring yields (x + 20)(x − 12) = 0, with solutions x = −20 and x = 12. Since a classroom dimension cannot be negative, the breadth is 12 m. Its length is 20 m, and the check 12 × 20 = 240 confirms both the equation and the units. Therefore option B is correct. The value 20 is the length, not the breadth. Values 10 and 15 would give lengths 18 and 23 respectively, producing areas 180 m² and 345 m², so they do not satisfy the stated 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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