Math, asked by sargi, 1 year ago

A path is 5 m wide runs inside a rectangular field.The length of rectangular field is three times the breadth of the field. If the area of the path is 500 m square ,then find the length and breadth of the field.

Answers

Answered by zeborg
55
Go through the solution and ask if you have any doubt at any step.

Hope this helps.
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Answered by mysticd
32

Answer:

Length = 45m

Breadth = 15m

Step-by-step explanation:

Dimensions of Rectangular field:

Let the breadth (B)=BC = x m

Length (L) = AB = 3x m

width of the road (w) = 5 m

Dimensions of inner rectangle:

length (l) = EF = L-2w

= 3x - 2×5

= (3x-10) m

breadth (b)=EH = B-2w

= (x-10) m

Given ,

Area of the path =500

=> Area of ABCD - Area of EFGH = 500

=> B - b=500

=> (3x)× x - (3x-10)(x-10)=500

=> 3x²-(3x²-30x-10x+100)=500

=> 3x²-3x²+30x+10x-100=500

=> 40x=500+100

=> 40x = 600

=> x = 600/40

=> x = 15

Therefore,

Length (L) = 3x = 3×15 = 45m

Breadth (B) = x = 15m

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