question_answer

The length and the breadth to a rectangular park are in the ratio 8 : 5. A path, 1.5m wide running all around the outside of the park has an area of \[594\,\,{{m}^{2}}.\]The dimensions of the park are

A)  120m, 75m      

B)  110m, 85m

C)  100 m, 95 m                

D)  None of these

Correct Answer: A

Solution :

Let the length and breadth of the park be 8x m  5x m, respectively,       \[\therefore \]Area of the park \[=(8x\times 5x){{m}^{2}}=40{{x}^{2}}{{m}^{2}}\] Length of park including the path\[=(8x+3)\,\,m\] Breadth of park including the path \[=(5x+3)\,\,m\] \[\therefore \]Area of the park including the path \[=(8x+3)(5x+3)\,\,{{m}^{2}}\] \[\therefore \]Area of the path \[=(8x+3)(5x+3)-40{{x}^{2}}=(39x+9)\,\,{{m}^{2}}\] \[\therefore \]\[39x+9=594\]\[\Rightarrow \]\[39x=585\]\[\Rightarrow \]\[x=15\] \[\therefore \] Length \[=(8\times 15)\,\,m=120\,\,m\] Breadth\[=(5\times 15)\,\,m=75\,\,m\]