A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire length of the fence measures 180 feet, how many feet long could the unfenced side of the rectangular park be?

If length of the field is 30 ft, then width is 120 ft.

If the  length of the field is 60 ft, then width is 60 ft.

Step-by-step explanation:

Let us assume the length of the rectangular park = L ft

Let us assume the breadth of the rectangular park = B  ft

Now, AREA of the given park =  L x B

⇒ L x B  = 3,600 sq ft   ... (1)

Also, the perimeter of three sides  = 180 ft

⇒ 2 L +  B  = 180  ..... (2)

Now, from (1) and (2), we get:

L x B  = 3,600

2 L +  B  = 180   ⇒ B  = 180 - 2 L

Substitute this in(1) , we get:

L x B  = 3,600   ⇒ L x (180 - 2 L)  = 3600

⇒ L = 30 or L  = 60

So, if L  = 30  ft , then B = 180 - 2L  =  180 - 60 = 120 ft

So, if L  = 60  ft , then B = 180 - 2L  =  180 - 120 = 60 ft

So, if length of the field is 30 ft, then width is 120 ft.

And if the  length of the field is 60 ft, then width is 60 ft.

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