Question

Two perpendicular cross roads of equal width run through the middle of a rectangular field of length 80 meter and breadth 60 meter. if the area of the cross roads is 675 m2, what is the width of the road:

Answer 1

If we take the width of each croass road to be x,

the area of one road = 80x and the area of the other is 60x

The area of the cross roads = 80x + 60x - x²

x² is the area of the centre where the two roads cross each other.

So'

80x + 60x - x² = 675

This simplifies to;

x² -140x + 675 = 0

x² -135x - 5x + 675 = 0

x(x - 135) -5(x - 135) = 0

(x - 5)(x - 135) = 0

either;

x -5 = 0, giving x = 5

or

x - 135 = 0, giving x = 135

The value of x can not be 135, because the length of the field is only 80m

So, the width of the roads = 5m

Answer 2

Solution :-

Area of the two perpendicular roads = 675 m² (given)

Let the width of the crossroad be x meter.

Then, 

80x + 60x - x² = 675 

⇒ x² - 140x + 675 = 0

⇒ x² - 135x - 5x + 675 = 0

⇒ x(x - 135) - 5(x - 135) = 0

⇒ (x - 135) (x - 5) = 0

⇒ x = 135 or x = 5

x = 135 is not possible.

So, x = 5 is the correct answer.

Hence, width of the road is 5 meter.

Answer.