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Question
The length and breadth of a rectangular field are in the ratio 8 : 5. A 2m wide path runs all around outside the field. The area of the path is 848m2. Find the length and breadth of the field.
Solution
Let the sides of the rectangular field = 8x and 5x
So, the sides of the rectangular field after leaving the path of 2m on all sides = 8x - 4 and 5x - 4
Area of the rectangular field = (8x) (5x)
Area of the rectangular field after leaving the path of 2m on all sides = (8x - 4)(5x - 4)
Area of the path of 2m on all sides
= (8x)(5x) - (8x - 4)(5x - 4)
= 40x2 - (40x2 - 32x - 20x + 16)
= 848
52x + 16 = 848
x = 16
The sides of the rectangular field
= 8x and 5x
= 128m and 80m.
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