Question

the length and the 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 305 sq.m. find the dimension of the park.​

Answer 1

Given that area of the park be 305m^2.

Let the length of the park be 5x m and breadth be 2x m.

Therefore,

Area of the rectangular park = (5x) x (2x)

= 10x^2 m^2

Width of the path = 2.5 m

From the figure,

Outer length PQ = 5x m + 2.5 m + 2.5 m

= (5x + 5) m

Outer breadth QR = 2x + 2.5 m + 2.5 m

= (2x + 5) m

Area of PQRS = (5x + 5) m x (2x + 5) m

= (10x2 + 25x + 10x + 25) m^2

= (10x2 + 35x + 25) m^2

Area of the path = [(10x^2 + 35x + 25) – 10x^2] m^2

By solving above equation we get

305 = 35x + 25

305 – 25 = 35x

280 = 35x

x = 280/35 = 8

Therefore,

Length of the park = 5x

= 5 x 8 = 40 m

Breadth of the park = 2x

= 2 x 8 = 16 m

Answer 2

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Given that area of the park be 305m^2.

Let the length of the park be 5x m and breadth be 2x m.

Therefore,

Area of the rectangular park = (5x) x (2x)

= 10x^2 m^2

Width of the path = 2.5 m

From the figure,

Outer length PQ = 5x m + 2.5 m + 2.5 m

= (5x + 5) m

Outer breadth QR = 2x + 2.5 m + 2.5 m

= (2x + 5) m

Area of PQRS = (5x + 5) m x (2x + 5) m

= (10x2 + 25x + 10x + 25) m^2

= (10x2 + 35x + 25) m^2

Area of the path = [(10x^2 + 35x + 25) – 10x^2] m^2

By solving above equation we get

305 = 35x + 25

305 – 25 = 35x

280 = 35x

x = 280/35 = 8

Therefore,

Length of the park = 5x

= 5 x 8 = 40 m

Breadth of the park = 2x

= 2 x 8 = 16 m