The length of a rectangle is 18 cm more than its breadth, and its area is 1240 square cm. What is the length of the rectangle?
Answer and explanation
Correct answer: \(9+\sqrt{1321}\) cm
Let the breadth of the rectangle be \(x\) cm. Its length is then \(x+18\) cm, so \(x(x+18)=1240\). Thus, \(x^2+18x-1240=0\), giving \(x=-9\pm\sqrt{1321}\). Since a dimension must be positive, the breadth is \(\sqrt{1321}-9\) cm and the length is \(x+18=9+\sqrt{1321}\) cm. Therefore, option D is correct. In an exam, select only the positive root for a physical dimension; 31 cm is not correct because \(31\times49=1519\), not 1240.
Frequently asked questions
What is the correct answer to this question?
\(9+\sqrt{1321}\) cm
Why is this the correct answer?
Let the breadth of the rectangle be \(x\) cm. Its length is then \(x+18\) cm, so \(x(x+18)=1240\). Thus, \(x^2+18x-1240=0\), giving \(x=-9\pm\sqrt{1321}\). Since a dimension must be positive, the breadth is \(\sqrt{1321}-9\) cm and the length is \(x+18=9+\sqrt{1321}\) cm. Therefore, option D is correct. In an exam, select only the positive root for a physical dimension; 31 cm is not correct because \(31\times49=1519\), not 1240.
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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