The difference between the length and breadth of a rectangle is 7 cm, and its area is 330 square cm. What is the perimeter of the rectangle?
Answer and explanation
Correct answer: 74 cm
Let the breadth be \(x\) cm. Then the length is \(x+7\) cm. Using the area, \(x(x+7)=330\), so \(x^2+7x-330=0\). Factoring gives \((x-15)(x+22)=0\). Thus \(x=15\) cm, since the negative root \(-22\) is not physically meaningful, and the length is \(22\) cm. Therefore, the perimeter is \(2(15+22)=74\) cm. Exam tip: In geometry word problems, reject any negative root because a length cannot be negative.
Frequently asked questions
What is the correct answer to this question?
74 cm
Why is this the correct answer?
Let the breadth be \(x\) cm. Then the length is \(x+7\) cm. Using the area, \(x(x+7)=330\), so \(x^2+7x-330=0\). Factoring gives \((x-15)(x+22)=0\). Thus \(x=15\) cm, since the negative root \(-22\) is not physically meaningful, and the length is \(22\) cm. Therefore, the perimeter is \(2(15+22)=74\) cm. Exam tip: In geometry word problems, reject any negative root because a length cannot be negative.
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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