The length n breadth of a rectglr field ia of ratio 6:4.

Question

 A 2.5m wide runing all along the outside of a field has an area of 825 sq.m. Find the perimeter of the field??

Answer 1

Let

Breath of rectangle = b

Length of rectangle = l

Width of outer path w = 2.5 m

Length : Breath = 6 : 4 ⇒ 4l = 6b ⇒ 2l = 3b

Area of field = lb

Total area including path = (l+2w)(b+2w) = lb + 2wl+2wb + 4w² = 4w² + w(2l+2b) + lb

Outer path Area A = Total area including path - Area os field

= 4w² + w(2l+2b) + lb - lb = 4w² + w(2l+2b) = 4(2.5)² + 2.5(3b+2b) = 4(6.25) + 2.5(5b) = 25 + 12.5b

Given Outer path Area A = 825 m²

25 + 12.5b = 825 ⇒ 12.5b = 825 - 25 ⇒ 12.5b = 800

b = 800/12.5 = 64 m

 

2l = 3b ⇒ 2l = 3*64 ⇒ 2l = 192

l = 192/2 ⇒ l = 96 m

 

Perimeter rectangular of the field P = 2(l+b)

P = 2(96+64) ⇒ 2(160) ⇒ 320 m

Solution : Perimeter rectangular of the field is 320 m.