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 416m2. The breadth (in m) of the field is

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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 416m². The breadth (in m) of the field is

A28

B14

C15

D16

Answer:

D. 16

Read Explanation:

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

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