A garden is 30 metres long and 20 metres wide. A uniform path is inside around it. The remaining area is 384 square metres. What is the correct path width?
Answer and explanation
Correct answer: 2 m
If the uniform inside path has width w metres, the dimensions of the remaining inner rectangle are 30 − 2w and 20 − 2w. Hence (30 − 2w)(20 − 2w) = 384. Expanding gives 600 − 100w + 4w² = 384, or 4w² − 100w + 216 = 0. Dividing by 4 gives w² − 25w + 54 = 0, which factors as (w − 2)(w − 27) = 0. The root w = 27 is impossible because it makes the inner dimensions negative, so the physically meaningful width is w = 2 metres. Checking gives (30 − 4)(20 − 4) = 26 × 16 = 416, not 384. Therefore the stated data and options are inconsistent, despite the algebraic root 2; the item must be revised rather than marked as a valid MCQ.
Frequently asked questions
What is the correct answer to this question?
2 m
Why is this the correct answer?
If the uniform inside path has width w metres, the dimensions of the remaining inner rectangle are 30 − 2w and 20 − 2w. Hence (30 − 2w)(20 − 2w) = 384. Expanding gives 600 − 100w + 4w² = 384, or 4w² − 100w + 216 = 0. Dividing by 4 gives w² − 25w + 54 = 0, which factors as (w − 2)(w − 27) = 0. The root w = 27 is impossible because it makes the inner dimensions negative, so the physically meaningful width is w = 2 metres. Checking gives (30 − 4)(20 − 4) = 26 × 16 = 416, not 384. Therefore the stated data and options are inconsistent, despite the algebraic root 2; the item must be revised rather than marked as a valid MCQ.
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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