Chapter 4: Quadratic Equations

Example 7. A rect angular field is 16m long and 10m wide, there is a path of uniform width all around it having an area of 120sq.m final the width of the path.

Solution:- Let width of the path be xm.

Area of the outer rectangle

= (16 + 2x) (10 + 2x)

= 160 + 32x + 20x + 4x²

= 160 + 52x + 4x2

Area of the inner rectangle

= 16m X 10m

= 160m²

Area of the path

= 160 + 52x + 4x² - 160 = 120

or, 4x² + 52x - 120 = 0

or, x² + 13x - 30 = 0

or, (x + 15) (x - 2) = 0

or, x = -15, 2

As width can not be negative x = 2 m

i. e. width of the path = 2 m