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A rectangular garden is fenced on three sides with a wall forming on the fourth side. The total length of the fence is 120m. The area of the garden is 1600m^2. Find the dimensions of the garden.

Respuesta :

Answer:

20m by 80m

Step-by-step explanation:

Let the dimension of the garden be x by y

The garden is fenced on three sides with a perimeter of 120m

Perimeter of the three sides = 2x+y

Therefore:

  • 2x+y=120

The Area of the garden = [tex]1600m^2[/tex]

  • xy=1600

From the first equation, y=120-2x

Substitute  y=120-2x into xy=1600

xy=1600

x(120-2x)=1600

[tex]120x-2x^2=1600\\2x^2-120x+1600=0\\2x^2-80x-40x+1600=0\\2x(x-40)-40(x-40)=0\\(2x-40)(x-40)=0\\2x-40=0\: x-40=0\\x=20 \: or \: x=40[/tex]

Recall,

xy=1600

When x=20, 20y=1600===>y=80

When x=40, 40y=1600===>y=40

So we have the pair (20,80) and (40,40).

However since we are told that the garden is rectangular, we pick the dimension with unequal sides.

The dimension of the garden is 20m by 80m.

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