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

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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:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”