Area of a rectangle is length times width. Let x = the width of the soccer field. That means the length of the field is x + 70.

Now take the formula for area to get A = x(x + 70)

We know area is 7,800 therefore,

7,800 = x(x + 60)

7,800 = x^2 + 70x

0 = x^2 + 70x - 7800

Factoring gives us

0 = (x + 130)(x - 60)

x = -130 or x = 60

Since we are talking about a length, x = -130 makes no sense, so the dimensions of the field are 60 by 130.

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