The length of a rectangle is 5 units more than its breadth, and its area is 204 square units. What is the length of the rectangle?
Answer and explanation
Correct answer: 17 इकाई
Let the breadth be \(x\) units. Then the length is \(x+5\) units. From the area, \(x(x+5)=204\), so \(x^2+5x-204=0\). Factoring gives \((x-12)(x+17)=0\); hence the positive breadth is \(12\) units and the length is \(12+5=17\) units. Thus, 12 units is the breadth, not the length. Exam tip: reject the negative root because a rectangle’s dimensions must be positive.
Frequently asked questions
What is the correct answer to this question?
17 इकाई
Why is this the correct answer?
Let the breadth be \(x\) units. Then the length is \(x+5\) units. From the area, \(x(x+5)=204\), so \(x^2+5x-204=0\). Factoring gives \((x-12)(x+17)=0\); hence the positive breadth is \(12\) units and the length is \(12+5=17\) units. Thus, 12 units is the breadth, not the length. Exam tip: reject the negative root because a rectangle’s dimensions must be positive.
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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