The area of a rectangle is 96 square units, and its length is 4 units more than its breadth. What is the breadth of the rectangle?
Answer and explanation
Correct answer: 8
Let the breadth be \(x\) units. Then the length is \(x+4\) units. Using the area, \(x(x+4)=96\), so \(x^2+4x-96=0\). Factoring gives \((x-8)(x+12)=0\), yielding \(x=8\) or \(x=-12\). Since a breadth cannot be negative, the correct answer is 8. Exam tip: In geometry word problems, reject any negative root because lengths must be positive.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Let the breadth be \(x\) units. Then the length is \(x+4\) units. Using the area, \(x(x+4)=96\), so \(x^2+4x-96=0\). Factoring gives \((x-8)(x+12)=0\), yielding \(x=8\) or \(x=-12\). Since a breadth cannot be negative, the correct answer is 8. Exam tip: In geometry word problems, reject any negative root because lengths 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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