The length and breadth of a rectangular park are in the ratio 5:2.A 2.5-m-wide path running all around the outside of the park has an area of 305m2.Find the dimensions of the park.
ANSWER IS l=40m,b=16m BUT I DONT KNOW THE SOLUTION.
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if the area is 305m^2 then
let the length of the rectangular park be 5x
∴ breadth will be 2x
so area= l*b
5x*2x
=10x²
width of the park all around the park=2.5m
∴lenght and breadth including path (5x+2.5 +2.5)m=(5x+5) and breadth of rectangular park=(2x+2.5+2.5)=(2x+5)
thus, area of the park=[(5x+2)(2x+5)-10x²]m²=(35x+25)m²
it is given that 35x +25 =305
⇒35x=280
x=8
thus the lenght of th park=5*8=40m and breadth of the park=2*8=16m
where *= ×
let the length of the rectangular park be 5x
∴ breadth will be 2x
so area= l*b
5x*2x
=10x²
width of the park all around the park=2.5m
∴lenght and breadth including path (5x+2.5 +2.5)m=(5x+5) and breadth of rectangular park=(2x+2.5+2.5)=(2x+5)
thus, area of the park=[(5x+2)(2x+5)-10x²]m²=(35x+25)m²
it is given that 35x +25 =305
⇒35x=280
x=8
thus the lenght of th park=5*8=40m and breadth of the park=2*8=16m
where *= ×
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