## Quadratic Equation Solution19

In this page quadratic equation solution19 we are going to see solution of the word problems of the topic quadratic equation.

Question 26

The footpath of uniform width runs all around a rectangular field 28 meters long and 22 meters wide. If the path occupies 600 m² area, find the width of the path.

Solution:

Let "x" be the width of the path

Length of the rectangular field = 28 m

Width of the rectangular field = 22 m

Area of the path = 600 Length of the larger rectangle = 28 + x + x = (28 + 2 x) m

Width of the larger rectangle = 22 + x + x = (22 + 2 x) m

Area of the path = Area of larger rectangle - Area of smaller rectangle

600 = (28 + 2 x)  (22 + 2 x) - 28 x 22

600 = 616 + 56 x + 44 x + 4 x² - 616

600 = 56 x + 44 x + 4 x²

600 = 4 x² + 100 x

4 x² + 100 x = 600

Now we are going to divide the whole equation by 4,so we get

x² + 25 x = 150

x² + 25 x - 150 = 0

x² + 30 x  - 5 x - 150 = 0

x (x + 30) - 5 (x + 30) = 0

(x - 5) (x + 30) = 0

x - 5 = 0         x + 30 = 0

x = 5               x = -30

Negative value is not possible. Because here x represents width of the path.

Therefore width of the path is 5 m

Verification:

Length of larger rectangle = 28 + 2 (5) = 38 m

Width of the larger rectangle = 22 + 2 (5) = 32 m

Area of path = Area of larger rectangle - Area of smaller rectangle

600 = 38 (32) - 28 (22)

600 = 1216 - 616

600 = 600

quadratic equation solution19