A square park has the same area as a rectangle. The side of the square is 48 m, while the rectangle has breadth \(x\) m and length \((x+28)\) m. What is the value of \(x\)?
Answer and explanation
Correct answer: 36
Since the areas are equal, \(x(x+28)=48^2=2304\). Thus, \(x^2+28x-2304=0\), which factors as \((x-36)(x+64)=0\). The roots are \(x=36\) and \(x=-64\). Since a breadth cannot be negative, the valid value is \(x=36\). Exam tip: In area-based word problems, form the equality first and reject any negative root that is not physically meaningful.
Frequently asked questions
What is the correct answer to this question?
36
Why is this the correct answer?
Since the areas are equal, \(x(x+28)=48^2=2304\). Thus, \(x^2+28x-2304=0\), which factors as \((x-36)(x+64)=0\). The roots are \(x=36\) and \(x=-64\). Since a breadth cannot be negative, the valid value is \(x=36\). Exam tip: In area-based word problems, form the equality first and reject any negative root that is not physically meaningful.
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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