A uniform border of width x metres is left along the inside of a square field. If the outer side of the field is 68 metres and the side of the remaining inner square is 44 metres, what is the value of x?
Answer and explanation
Correct answer: 12 m
The border is removed once from each of the two opposite sides, so the inner side is 68 - 2x. Thus, 68 - 2x = 44, giving 2x = 24 and x = 12 metres. The total difference of 24 metres cannot be taken directly as x because it represents two border widths. Exam tip: For a uniform inner border of width x, the difference between the outer and inner sides is always 2x.
Frequently asked questions
What is the correct answer to this question?
12 m
Why is this the correct answer?
The border is removed once from each of the two opposite sides, so the inner side is 68 - 2x. Thus, 68 - 2x = 44, giving 2x = 24 and x = 12 metres. The total difference of 24 metres cannot be taken directly as x because it represents two border widths. Exam tip: For a uniform inner border of width x, the difference between the outer and inner sides is always 2x.
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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