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The length and breadth of a rectangular field are in the ratio 7 : 4. A path 4 m wide running all around outside has an area of 416 m² . The breadth (in m) of the field is
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- 28
- 14
- 15
- 16
- 28
Correct Option: D
Let length of rectangular field = 7x metre & breadth = 4x metre
Length of field with path = (7x + 8) metre
Breadth = (4x + 8) metre
∴ Area of path = (7x + 8) × (4x + 8) – 7x × 4x
= 28x² + 32x + 56x + 64 – 28x²
= 88x + 64
∴ 88x + 64 = 416
⇒ 88x = 416 – 64 = 352
⇒ x = 4
∴ Breadth of field = 16 metre
Here, L = 7x, B = 4x
w = 4 m,
Area of path = 2w [L + B + 2w]
416 = 2 × 4 (7x + 4x + 2 × 4)
416 = 8 (11x + 8)
52 = 11x + 8
11x = 44 x
= 4
∴ Breadth of field = 4 × 4 = 16 m
