A square park has the same area as a rectangle. The side of the square is 56 m, while the rectangle has breadth \(x\) m and length \((x+66)\) m. What is the value of the rectangle’s breadth \(x\)?
Answer and explanation
Correct answer: 32 m
The square’s area is \(56^2=3136\) square metres. Equating the two areas gives \(x(x+66)=3136\), or \(x^2+66x-3136=0\). Factoring, \((x-32)(x+98)=0\), so \(x=32\) or \(x=-98\). Since a rectangle’s breadth must be positive, \(x=32\) m is the valid answer. In word problems, always reject roots that do not have a meaningful physical interpretation.
Frequently asked questions
What is the correct answer to this question?
32 m
Why is this the correct answer?
The square’s area is \(56^2=3136\) square metres. Equating the two areas gives \(x(x+66)=3136\), or \(x^2+66x-3136=0\). Factoring, \((x-32)(x+98)=0\), so \(x=32\) or \(x=-98\). Since a rectangle’s breadth must be positive, \(x=32\) m is the valid answer. In word problems, always reject roots that do not have a meaningful physical interpretation.
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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