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.

Answer 1

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.