The length of a rectangle is 3 cm more than its breadth, and its area is 180 square cm. What is the breadth of the rectangle?
Answer and explanation
Correct answer: 12 cm
Let the breadth of the rectangle be \(x\) cm. Its length is then \(x+3\) cm. Using the area, \(x(x+3)=180\), so \(x^2+3x-180=0\). Factoring gives \((x+15)(x-12)=0\), hence \(x=12\) or \(x=-15\). Since a length cannot be negative, \(-15\) is rejected and the breadth is 12 cm. Exam tip: In geometrical word problems, discard any negative root because dimensions must be positive.
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What is the correct answer to this question?
12 cm
Why is this the correct answer?
Let the breadth of the rectangle be \(x\) cm. Its length is then \(x+3\) cm. Using the area, \(x(x+3)=180\), so \(x^2+3x-180=0\). Factoring gives \((x+15)(x-12)=0\), hence \(x=12\) or \(x=-15\). Since a length cannot be negative, \(-15\) is rejected and the breadth is 12 cm. Exam tip: In geometrical word problems, discard any negative root because dimensions 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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