A square field has an outer side of 52 m. After leaving a uniform strip of equal width on all four sides, the inner square has a side of 36 m. What is the width \(x\) of the strip?
Answer and explanation
Correct answer: 8 m
The strip is removed from both opposite sides, so the inner side is \(52-2x\). Therefore, \(52-2x=36\), giving \(2x=16\) and \(x=8\) m. Using areas gives the equivalent quadratic equation \((52-2x)^2=36^2\); the geometrically valid root is \(x=8\). Exam tip: divide the difference between the outer and inner side lengths by 2. For example, 10 m would reduce the inner side to 32 m, not 36 m.
Frequently asked questions
What is the correct answer to this question?
8 m
Why is this the correct answer?
The strip is removed from both opposite sides, so the inner side is \(52-2x\). Therefore, \(52-2x=36\), giving \(2x=16\) and \(x=8\) m. Using areas gives the equivalent quadratic equation \((52-2x)^2=36^2\); the geometrically valid root is \(x=8\). Exam tip: divide the difference between the outer and inner side lengths by 2. For example, 10 m would reduce the inner side to 32 m, not 36 m.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
