Question

1)a farmer wishes to grow a hundred metre square rectangle corn field. he has only 30 metre wire, he fences 3 side of the rectangular Garden Letting compound wall of the house act as fourth side fence. find the dimension of the garden garden

Answer 1

Answer:

Given :-

• Area of corn field = 100 m^2

• Perimeter of three sides is = 30 m

What to find out = Dimension of the garden?

Solution :-

Let the length of one side be = x meters

and other side be = y meters.

As question :-

x + y + x = 30

⇒ y = 30 – 2x .... [equation 1]

∵ Area of the corn field = 100 m^2

∴ Area of square = side times side= (xy)

⇒ xy = 100

⇒ xy = 100

⇒ x (30 – 2x) = 100 [from equation 1]

⇒ 30x – 2x^2 = 100

⇒ 15x – x^2 = 50

⇒ x^2 – 15x + 50 = 0

Now, Factorise it by splitting middle term

⇒ x2 – 10x – 5x + 50 = 0

⇒ (x – 10) (x – 5) = 0

We get two values of X

⇒ x = 5, 10

Hence,

When x = 5

we have, y = 30 – 2 x 5 = 20 m

When x = 10

we have, y = 30 – 2 x 10= 10 m

Hence, the dimensions of the corn field are :-

5 m x 20 m = 100 m^2

or

10 m x 10 m= 100 m^2 Answer

*Shape of dimension is= Rectangular or Square