In this page quadratic equation practical solution4 we are going to see solution of practice question of the worksheet quadratic equation practical application.

Question 4 :

A rectangular field is 20 m long and 14 m wide. There is the path of equal width all around it having an area of 111 sq.meters. Find the width of the path on the outside.

Solution:

Length of the rectangular field = 20 m

Width of the rectangular field = 14 m

Let x be the uniform width all around the path

Length of the rectangular field including path = 20 + x + x

= 20 + 2 x

Width of the rectangular field including path = 14 + x + x

= 14 + 2 x

Area of path = Area of rectangular field including path - Area of rectangular field

111 = (20 + 2 x) (14 + 2 x) -  (20 x 14)

111 = 280 + 40 x + 28 x + 4 x² – 280

111 = 68 x + 4 x²

4 x² + 68 x - 111 = 0

4 x² + 68 x - 111 = 0

(2 x + 37) (2 x  - 3) = 0

2 x + 37 = 0                        2 x – 3 = 0

2 x = - 37                         2 x = 3

x = -37/2                          x = 3/2

x = -18.5                           x = 1.5 m

Therefore width of the path = 1.5 m

Verification:

111 = (20 + 2 x) (14 + 2 x) -  (20 x 14)

111 = (20 + 2(3/2)) (14 + 2(3/2)) – (20 x 14)

111 = (20 + 3) (14 + 3) – 280

111 = (23)(17) – 280

111 = 391 – 280

111 = 111

Question 6     Question 7     Question 8     Question 9     Question 10

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: