Question

A rectangular plot 50 m long 38 m wide and area of path is 492 find the width of path

Answer 1

Let the width of the path be x then :

Length of outer rectangle : 50 + 2x

Width of the outer rectangle : 38 + 2x

Area of the outer rectangle is :

(50 + 2x) (38 + 2x) = 1900 + 76x + 100x + 4x²

4x² + 176x + 1900

Area of the field is :

50 × 38 = 1900

The difference between the areas give the area of the path.

(4x² + 176x + 1900) - 1900 = 4x² + 176x

4x² + 176x = 492

4x² + 176x - 492 = 0

Dividing through by 4

x² + 44x - 123 = 0

Solving for x

We will use the quadratic formula :

{-44 +/-√44² - (4 × - 123)} / 2

(-44 +/- 49.27) / 2 = 2.635 or - 46.635

We take the positive value since length is positive.

The width of the path is thus 2.635 m