A path 5 m wide runs alongside a rectangular field.The length of the rectangular field is three times the breadth of the field.If the area of the path is 500*500 m.Find the length and breadth of the field
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Length = 45m
Breadth = 15m
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 m²
=> Area of ABCD - Area of EFGH = 500
=> L×B - l×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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