The length and breadth of a rectangular park are in the ratio 5:2.A 2.5m wide path running all around the outside of the park has an area of 305m. Find the dimensions of the park.
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Answer:
Dimensions of the park are 40m and 16m.
Step-by-step explanation:
Let 5:2 be 5x and 2x.
Area of a rectangular park = 5x × 2x = 10x²
The wide path has an area of 305 m² and it is 2.5m wide.
So the Length of the rectangular park including the path = (5x+2×2.5)m=(5x+5)m
The breadth of the rectangular park including the path = (2x+2×2.5)m=(2x+5)m
Area of The rectangular park including the path = (5x+5) × (2x+5)
=5x(2x+5) + 5(2x+5)
=10x²+25x+10x+25
=10x²+35x+25
We know,
Area of Rectangular Park including the path - Area of Rectangular Park = Area of Path
So, ATP,
(10x²+35x+25)-10x²=305
10x²-10x²+35x+25=305
35x+25=305
35x=280
x=280/35
x=8
Length of the park = 5×8=40m
Breadth of the park = 2×8=16m
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