Aptitude - Area - Discussion

@Ayoosh,

60 and 40 are not the lengths of the roads. 60 is the length and 40 is the width. Still, have a confusion. Could anyone please explain it clearly?

Thank you @Ayoosh.

God job @Ayoosh.

(60x + 40x -x^2 this is the area of cross roads alone. 60 and 4O are lengths of cross roads and x is the breadth.

X^2 is subtracted because the meeting of crossroads, the calculated area overlaps. So - X^2.

Great explanation @Ayoosh.

We can also subtract the width of the road from length and breadth of the road and multiply the values to get the area of the lawn i.e.

Let the width be x.

Length of lawn = 60 - x.

Breadth of lawn = 48 - x.

(60 - x) (40 - x) = 2109. As given in question.

X^2 - 100x - 291 = 0.

X = 3 and 97.

The value 3 is there in the given option. So, width of the road is 3m.

@Puskar,

You may go through Diego's answer for better understanding.

Guys! it should be 2x^2 instead of simply x^2? don't you all agree?

@Rkbm your answer best answer.

So it is a rectangle of 60x40cm. It has 2 crossroads, therefore the area of the roads is the horizontal one: 60 times the with (x). -->60*x plus the vertical road 40*x. This results in 60x+40x but you are adding 2 times the area where the roads intersect (one time for the vertical road and one time for the horizontal road). The double counted area is x*x = x^2. So if you subtract this area from 60x+40x you will eliminare 60x+40x -x^2.

                       60cm
_______________________________
I     LAWN        I RD I       LAWN          I
I______________I____I________________I
I    ROAD         I       I      ROAD          I
I_____________  IX^2I________________I  40cm
I     LAWN        I       I       LAWN         I
I______________I RD I________________I

Hope this helps you better understand the problem.