The length of a rectangle is 16 cm more than its breadth, and its area is 2145 square cm. What is its length?
Answer and explanation
Correct answer: 55 cm
Let the breadth of the rectangle be \(x\) cm. Its length is then \(x+16\) cm. Using the area, \(x(x+16)=2145\), so \(x^2+16x-2145=0\). Factoring gives \((x-39)(x+55)=0\). Since a breadth cannot be negative, \(x=39\) cm. Therefore, the length is \(39+16=55\) cm. Exam tip: reject any negative root when the variable represents a physical dimension.
Frequently asked questions
What is the correct answer to this question?
55 cm
Why is this the correct answer?
Let the breadth of the rectangle be \(x\) cm. Its length is then \(x+16\) cm. Using the area, \(x(x+16)=2145\), so \(x^2+16x-2145=0\). Factoring gives \((x-39)(x+55)=0\). Since a breadth cannot be negative, \(x=39\) cm. Therefore, the length is \(39+16=55\) cm. Exam tip: reject any negative root when the variable represents a physical dimension.
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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