Question

a footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide .if the path occupies 208m2,find the width of the foothpath

Answer 1

length=32 m
breadth=24 m
area of park = l×b
                    = 32×24
                    = 768 m²
outer area of path= 208 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

Answer 2

Answer:

I hope it works for you

Step-by-step explanation:

Length=32

Breadth = 24

area of park = 1×b

=32×24

=768m²

area of path = 208m²

Let the width of the path be 'w' meters

Inner lenth 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- 112w+768)=208

4w2-112w + 208 =0

w2- 28w+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 2m

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