A rectangular field is 25 metres long and 15 metres wide. A uniform path is constructed outside it on all sides. If the total area including the path is 651 square metres, what is the width of the path?
Answer and explanation
Correct answer: 3 metres
Let the uniform outside-path width be x metres. The path adds x metres on each side, so the outside rectangle has length 25 + 2x and width 15 + 2x. Its area therefore satisfies (25 + 2x)(15 + 2x) = 651. Expanding gives 4x² + 80x + 375 = 651, or 4x² + 80x − 276 = 0; dividing by 4 gives x² + 20x − 69 = 0. This factors as (x − 3)(x + 23) = 0. The width must be positive, so x = 3. Checking gives outside dimensions 31 m and 21 m, with area 31 × 21 = 651. Thus option A is correct; the other options fail the area condition.
Frequently asked questions
What is the correct answer to this question?
3 metres
Why is this the correct answer?
Let the uniform outside-path width be x metres. The path adds x metres on each side, so the outside rectangle has length 25 + 2x and width 15 + 2x. Its area therefore satisfies (25 + 2x)(15 + 2x) = 651. Expanding gives 4x² + 80x + 375 = 651, or 4x² + 80x − 276 = 0; dividing by 4 gives x² + 20x − 69 = 0. This factors as (x − 3)(x + 23) = 0. The width must be positive, so x = 3. Checking gives outside dimensions 31 m and 21 m, with area 31 × 21 = 651. Thus option A is correct; the other options fail the area condition.
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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