Aptitude - Area - Discussion

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.

Consider the width of road as "x".

Now, the area of the lawn = (60 - x)(40 - x) = 2109.
=> 2400 - 60x - 40x + x^2 = 2109,
=> -60x - 40x + x^2 = -2400 + 2109.
=> -(60x + 40x) + x^2 = -291.
=> x^2 - 100x + 291 = 0.
=> (x - 97)(x - 3) = 0
=>x = 3.

40 X is width of the road.....
_________ We have already find out the area of the road by
| | | | subtracting (total area -lawn area)...
|___| |___| road area == 291 sq units
|___| |___|60 i.e Area of two triangle(roads)-(overlap btwn them)
| | | | over lap is width^2====x^2
|___|_|___| area of two triangle (60*x) and (40*x)
|x| so (60x+40x)-x^2===291
| | by solving tis v can find x===3

For all having probs in the 60x + 40x - x^2!!!!

See road is a rect. and they are intercrossing. let the width be x, then for one road area will be 40x and for the other road will be 60x since 60 and 40 will be the lengths of road.

now, we area of roads is 291 m², so

ar(road1) + ar(road2) - ar(intercrossing)
60x + 40x - x^2 = 291 and then on you can find the ans

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.

See road is a rect. and they are intercrossing. let the width be x, then for one road area will be 40x and for the other road will be 60x since 60 and 40 will be the lengths of road.

Now, we area of roads is 291 m², So

area(road1) + area(road2) - area(intercrossing).

60x + 40x - x^2 = 291 and then on you can find the answer.

When two roads intersecting like a +.
So road 1 area is l*b =60*x rectangle road 2 area is l*b =40*x rectangle intersecting place is in a square shape so side =x.; the area is x^2.

In road 1 and road2 we are calculating intersecting point area two times so we have to Subtract that square shape intersecting point.

Area of the park = (60 x 40) m2 = 2400 m2.

Area of the lawn = 2109 m2.

Area of the crossroads = (2400 - 2109) m2 = 291 m2.

Let the width of the road be x metres. Then,

60x + 40x - x2 = 291.

x2 - 100x + 291 = 0.

(x - 97)(x - 3) = 0.

x = 3.

hey golu..
we have two options for the value of 'x' :
x=97 or x=3;
97 is not chosen as value of 'x' because the width of the rectangular park is only 40 m.
and only the value 'x=3' is less than 40 m.
so, 'x=97' is not possible at all.

The intersection part area should be subtracted it's area = x^2.
Area of one road along length = 40x.
Area of one road along breadth = 60x.
But the area of roads is 2400-2109 = 291.
So 40x+60x-x^2 = 291.
Solve, we get x=3.