Question

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 305 m2. Find the dimensions of the park.
​

Answer 1

Answer:

Let the length of the park=5a and its breadth =2a

∴ Area of the rectangular park=5a×2a=10a

2

Width of the park=2.5

Outer length PQ=5a+2.5+2.5=5a+5

Outer length QR=2a+2.5+2.5=2a+5

Area of PQRS=(5a+5)(2a+5)=10a

2

+35a+25

Area of the path=10a

2

+35a+25−10a

2

⇒305=35a+25

⇒35a=305−25=280

∴a=

35

280

=8

∴ Length of the park=5a=5×8=40m

Breadth of the park=2a=2×8=16m

Answer 2

Answer:

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Step-by-step explanation:

Let the length of the park=5a and its breadth =2a

∴ Area of the rectangular park=5a×2a=10a

2

Width of the park=2.5

Outer length PQ=5a+2.5+2.5=5a+5

Outer length QR=2a+2.5+2.5=2a+5

Area of PQRS=(5a+5)(2a+5)=10a

2

+35a+25

Area of the path=10a

2

+35a+25−10a

2

⇒305=35a+25

⇒35a=305−25=280

∴a=

35

280

=8

∴ Length of the park=5a=5×8=40m

Breadth of the park=2a=2×8=16m

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