Question

a rectangular field is 20m long and 14m wide. There is a path of equal width all around it, having an area of 111 sq. Mtrs. Find the width of the path

Answer 1

First we will find the area of rectangular field:

20m×14m
=280m^2

Now subtracting the area of rectangular field by the path:

280sq.m-111sq.m
=169sq.m


Therefore the width of the path is 169sq.m

Thank you

Answer 2

Answer:

Step-by-step explanation:

Solution:-

Let the width of the path be x m.

Then, the length of the path be 20 + 2x m.

And the width of the path be 14 + 2x m.

According to the Question,

Area of rectangular path = Length × Breadth

= (20 + 2x) (14 + 2x)

= 4x² + 68x + 280  

Area of the path = 111 m²

⇒ 4x² + 68x + 280  = 111 m²

Subtracting 280 from left side,

⇒ 4x² + 68x + 280 - 280  = 111 m²

⇒ 4x² + 68x = 111 m²

⇒ 4x² + 68x - 111 = 0

⇒ 4x² + 74x - 6x - 111 = 0

⇒ 2x(2x + 37) - 3(2x + 37) = 0

⇒ (2x + 37) (2x - 3) = 0

⇒ x = - 37/2, 3/2 = 0

⇒ x = - 18.5, 1.5 (As x can't be negative)

⇒ x = 1.5 m

Hence, the width of the path is 1.5 m.