In this page quadratic equation practical solution3 we are going to see solution of practice question of the worksheet quadratic equation practical application.

Question 3:

A farmer wishes to start a 100 sq.m rectangular vegetable garden. Since he has only 30 m barbed wire, he fences the sides of the rectangular garden letting his house compound wall act s the fourth side fence. Find the dimension of the garden.

Solution:

Let “x” and “y” are the dimension of the vegetable garden

Area of rectangle = Length x width

x x y = 100

x = 100/y

We are going to cover the barbed wire for fencing only. So it must be the perimeter of vegetable garden. Usually perimeter always covers all the four sides. But here we are going to cover only three sides. Because one side of the vegetable garden will act as the compound wall.

x + x + y = 30

2 x + y = 30

2(100/y) + y = 30

(200/y) +  y = 30

(200 + y²)/y = 30

200 + y² = 30 y

y² - 30 y + 200 = 0

y² - 10 y – 20 y + 200 = 0

y (y – 10) – 20 (y – 10) = 0

(y – 10) (y – 20) = 0

y – 10 = 0     y – 20 = 0

y = 10          y = 20

Now we are going to apply these values in x = 100/y to get the values of x

If  y = 10                                            if y = 20

x =100/10                                            x = 100/20

x = 10 m                                               x = 5 m

Therefore the required dimensions are 10 m ,10 m  or 20 m , 5 m

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