Question

A path of uniform width runs round the inside of a rectangular field 38m long and 32m wide if the path occupies area 600m. Then find the width of the path???

Answer 1

Outer length of the rectangular field = 32 m
Outer breadth of the rectangular field = 24 m

Outer Area = 32 x 24 = 768 m2
Let the width of the path be 'w' meters

Inner length of the rectangular field = (32 - 2w) m
Inner breadth of the rectangular field = (24 - 2w) m
Inner area = (32 - 2w)(24 - 2w) = 4w2 - 112 w + 768
Area of the path = Outer area - Inner area = (768) - (4w2 - 112 w + 768) = 208
⇒ 4w2 - 112 w + 208 = 0
⇒ w2 - 28 w + 52 = 0
⇒ (w - 26)(w - 2) = 0
⇒ w = 26 or 2
Since the outer breadth of the field is 24 m, breadth of the rectangular field is 2 m
Plzz mark me as brainlistt