Question

the length and breadth of a rectangular Park are in the ratio 5 is to 2 a wide path of 2.5 metre that runs All Around has an area 445 square metre. find the dimensions of the park

Answer 1

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

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

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  square +35a+25

Area of the path=10a  square +35a+25−10a  square

⇒305=35a+25

⇒35a=305−25=280  

∴a=   280 /35

=8

∴ Length of the park=5a=5×8=40m

Breadth of the park=2a=2×8=16m