Question

The length and breadth of a rectangular park are in ratio 8:5.A path 1:5m wide, running all around the outside of park has an area of 594m2 . Find the dimension of the park.

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Answer 1

Answer:

Solution

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Let the length of the park rectangle ABCD be 8x m

Let the breadth of the park rectangle ABCD be 5x m

Area of rectangle ABCD=(8x×5x)m

                                     =40x  

2

m

Length of the park including path PQRS

                                     =8x+2(width of path)

                                     =8x+2(1.5)

                                     =8x+3m

Breadth of the park including path PQRS

                                     =5x+2(width of path)

                                     =5x+2(1.5)

                                     =5x+3m

Area of the park including path PQRS

                                     =(8x+3)(5x+3)

                                     =(40x  

2

+39x+9)m  

2

 

Given,

Area of the path=594m  

2

 

Area of PQRS-Area of ABCD=594

    =>40x  

2

+39x+9−40x  

2

=594

                               =>39x=594−9

                               =>39x=585

                               =>x=  

39

585

​

 

                               =>x=15

           

           Length of the park=8x

                                         =8×15

                                         =120m  

           Breadth of the park=5x

                                          =5×15

                                          =75m

Step-by-step explanation:

Answer 2

l=120m

b=75 m.

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