The area of a rectangle is 720 square cm, and its length is 6 cm more than its breadth. What is the perimeter of the rectangle?
Answer and explanation
Correct answer: 108 cm
Let the breadth be x cm. Then the length is (x+6) cm. Using the area, \(x(x+6)=720\), or \(x^2+6x-720=0\). The positive solution is \(x=24\), so the breadth is 24 cm and the length is 30 cm. Hence, the perimeter is \(2(24+30)=108\) cm, making option B correct. Exam tip: use length × breadth for area and \(2(\text{length}+\text{breadth})\) for the perimeter of a rectangle.
Frequently asked questions
What is the correct answer to this question?
108 cm
Why is this the correct answer?
Let the breadth be x cm. Then the length is (x+6) cm. Using the area, \(x(x+6)=720\), or \(x^2+6x-720=0\). The positive solution is \(x=24\), so the breadth is 24 cm and the length is 30 cm. Hence, the perimeter is \(2(24+30)=108\) cm, making option B correct. Exam tip: use length × breadth for area and \(2(\text{length}+\text{breadth})\) for the perimeter of a rectangle.
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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