Given that the area of the rectangular field is 15,000 sq. ft and it's width is 470 ft less than the length of the of the field, the dimensions of the field would be:
Recall:
Given:
Required:
Thus, using the area formula, the equation below is derived:
[tex](l)(l - 470) = 15,000[/tex]
[tex]l^2 - 470l = 15,000\\\\l^2 - 470l - 15,000 = 0\\\\[/tex]
[tex](l + 30)(l - 500) = 0\\\\[/tex]
[tex]l = -30 $ or $ l = 500[/tex]
We will go with the positive value, which is 500.
Therefore, the length of the rectangular field is 500 ft.
Width = l - 470
Width = 500 - 470
Width = 30 ft
Therefore, given that the area of the rectangular field is 15,000 sq. ft and it's width is 470 ft less than the length of the of the field, the dimensions of the field would be:
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