The length of a rectangular book cover is 3 cm more than its breadth. If the area of the cover is 154 square cm, what is its breadth?
Answer and explanation
Correct answer: 11 cm
Let the breadth be \(x\) cm. Then the length is \(x+3\) cm. Using the area formula, \(x(x+3)=154\), so \(x^2+3x-154=0\). Factoring gives \((x-11)(x+14)=0\), yielding \(x=11\) or \(x=-14\). Since length and breadth must be positive, \(-14\) is not physically valid. Therefore, the breadth is 11 cm. Exam tip: In dimension-based word problems, reject any negative root.
Frequently asked questions
What is the correct answer to this question?
11 cm
Why is this the correct answer?
Let the breadth be \(x\) cm. Then the length is \(x+3\) cm. Using the area formula, \(x(x+3)=154\), so \(x^2+3x-154=0\). Factoring gives \((x-11)(x+14)=0\), yielding \(x=11\) or \(x=-14\). Since length and breadth must be positive, \(-14\) is not physically valid. Therefore, the breadth is 11 cm. Exam tip: In dimension-based word problems, reject any negative root.
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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