the length and breadth of a rectangular park are in the ratio 5:3.a 2.5 m wide running all around the outside of the park has an area 305m^2. Find the dimensions of the park.
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Answer:
Let the length of the park=5a and its breadth =2a
∴ Area of the rectangular park=5a×2a=10a2
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)=10a2+35a+25
Area of the path=10a2+35a+25−10a2
⇒305=35a+25
⇒35a=305−25=280
∴a=35280=8
∴ Length of the park=5a=5×8=40m
Breadth of the park=2a=2×8=16m
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