question_answer

A rectangular park 60 metre long and 40 metre wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 metre2 then the width of the road is

A)  3 metre   

B)  5 metre

C)  6 metre                        

D)  2 metre

Correct Answer: A

Solution :

(a): Area of rectangular park \[=60\times 40=2400\]sq. metre Let the width of cross road be\[x\]metre. \[\therefore \] Area of cross roads \[=60x+40x-{{x}^{2}}\] \[=100x-{{x}^{2}}\] According to the question. \[100x-{{x}^{2}}=2400-2109\] \[\Rightarrow \]\[100x-{{x}^{2}}=291\] \[\Rightarrow \]\[{{x}^{2}}-100x+291=0\] \[\Rightarrow \]\[{{x}^{2}}-3x-97x+291=0\] \[\Rightarrow \]\[x\left( x-3 \right)-97\left( x-3 \right)=0\] \[\Rightarrow \]\[\left( x-3 \right)\left( x-97 \right)=0\] \[\Rightarrow \] \[x=3\] because \[x\ne 97\]