The length of a rectangle is 12 cm more than its breadth, and its area is 864 square cm. What is the length of the rectangle?
Answer and explanation
Correct answer: 36 cm
Let the breadth of the rectangle be \(x\) cm. Then its length is \(x+12\) cm. Using the area, \(x(x+12)=864\), so \(x^2+12x-864=0\). Factoring gives \((x-24)(x+36)=0\). Thus \(x=24\), since \(-36\) cannot represent a dimension, and the length is \(24+12=36\) cm. Therefore, option C is correct. Exam tip: In dimension problems, reject any negative root because lengths and breadths must be positive.
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What is the correct answer to this question?
36 cm
Why is this the correct answer?
Let the breadth of the rectangle be \(x\) cm. Then its length is \(x+12\) cm. Using the area, \(x(x+12)=864\), so \(x^2+12x-864=0\). Factoring gives \((x-24)(x+36)=0\). Thus \(x=24\), since \(-36\) cannot represent a dimension, and the length is \(24+12=36\) cm. Therefore, option C is correct. Exam tip: In dimension problems, reject any negative root because lengths and breadths must be positive.
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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