The length of a rectangle is 19 cm more than its breadth, and its area is 2772 square cm. What is the length of the rectangle?
Answer and explanation
Correct answer: 63 cm
Let the breadth be \(x\) cm. Then the length is \(x+19\) cm. Using the area, \(x(x+19)=2772\), so \(x^2+19x-2772=0\). Factoring gives \((x-44)(x+63)=0\). Thus \(x=44\) cm, since a negative dimension is not possible, and the length is \(44+19=63\) cm. Exam tip: Reject negative roots when solving quadratic equations involving physical dimensions.
Frequently asked questions
What is the correct answer to this question?
63 cm
Why is this the correct answer?
Let the breadth be \(x\) cm. Then the length is \(x+19\) cm. Using the area, \(x(x+19)=2772\), so \(x^2+19x-2772=0\). Factoring gives \((x-44)(x+63)=0\). Thus \(x=44\) cm, since a negative dimension is not possible, and the length is \(44+19=63\) cm. Exam tip: Reject negative roots when solving quadratic equations involving physical dimensions.
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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