Question

a rectangular field is 20m long and 14m wide. There is a path of equal width all around it, having an area of 72 sq. Mtrs. Find the width of the path

Answer 1

Let the width of the path be x.

The length and width of the outer rectangle is :

Length : 20 + 2x

Width : 14 + 2x

The area of the outer rectangle is :

(14 + 2x)(20 + 2x) = 4x² + 68x + 280

The area of the field :

14 × 20 = 280m²

The area of the path is the difference between the two areas :

(4x² + 68x + 280) - 280 = 4x² + 68x

4x² + 68x = 72

4x² + 68x - 72 = 0

Divide through by 4

X² + 17x - 18 = 0

Solving for x :

The roots are : - 1 and 18

x ² - x + 18x - 18 = 0

x (x - 1) + 18(x - 1) = 0

(x - 1)(x + 18) = 0

x = 1 or - 18

We take 1 since it is positive and length is positive.

Length of the path is 1 m.

Answer 2

Answer:

Width of road = 1 m

Step-by-step explanation: