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The length and breadth of a rectangular park are in the ratio 5:2 a 2.5 m path running all around the outside of the park has an area of $305 m^{2}$ Find the dimensions of the park.

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16 m and 40 m

20 m and 30 m

25 m and 20 m

35 m and 10 m

answer is A.

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Detailed Solution

Given,
Area of the park=

305 m^{2}

Length and breadth ration of park =5:2
Let length of the park =5x
Breadth of the park=2x
Width of the path =2.5 m
From the figure,

TD = DU = VC = WC = XA = AO = BN = BM = 2.5 m

Also,

SR = UW = XM = PQ

C:UserssoftberryDownloadsP0041 JPEGQ.73.jpg

And

SP = TO = VN = RQ

CB = AD = 2 x

DC = AB = 5 x

Then,

UW = XM = 5 x + 5

Therefore
Rectangle UWRS area= Rectangle XMQP area
And also
Rectangle UDAX area = Rectangle CWMB area
Thus
Area of Path = Area of UDAX + Area of CWMB + Area of XMQP + Area of UWRS
Area of Path = 2(Area of UDAX + Area of XMQP)
Now Area of

UDAX,

= UD \times AX = 2 x \times 2.5 = 5 x

Also, the Area of

XMQP = XM \times MQ = 2.5 (5 x + 5)

\Rightarrow 305 = 2 \{2.5 (5 x + 5) + 5 x\}

\Rightarrow 305 = 5 (5 x + 5) + 10 x

\Rightarrow 305 = 25 x + 25 + 10 x

\Rightarrow 305 = 35 x + 25

\Rightarrow 280 = 35 x

\Rightarrow x = 8

Put

x = 8

in 5x and 2x to calculate the value of length and breadth.
Length=

5 x

= 5 \times 8

= 40

m
Breadth =

2 x

2 \times 8 = 16

Hence, the dimensions of the rectangular park are 16 m and 40 m
Correct option is 1.

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