question_answer

A path of uniform width runs round the inside of a rectangular field 38 m long and 32 m wide. If the path occupies \[600\,\,c{{m}^{2}}\] then the width of the path is

A)  5 m                 

B)  8 m

C)  7.5 m  

D)  9 m

Correct Answer: A

Solution :

[a]        Let the width of path = x m \[\therefore \] \[(38-2x)(32-2x)=616\] \[1216-140x+4{{x}^{2}}=616\] \[4{{x}^{2}}-140x+600=0\] \[{{x}^{2}}-35x+150=0\] \[\therefore \] \[x=30,\] \[x=5\] Hence, the width of path = 5 m