Answer :
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:
- Length = 500 ft
- Width = 30 ft
Recall:
- Area of rectangle: A = length x width
Given:
- Area of rectangular field = 15,000 sq. ft
- length = l
- width = l - 470
Required:
- Dimensions of the field (the length and the width).
Thus, using the area formula, the equation below is derived:
[tex](l)(l - 470) = 15,000[/tex]
- Solve for l
[tex]l^2 - 470l = 15,000\\\\l^2 - 470l - 15,000 = 0\\\\[/tex]
- Factorize
[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
- Plug in the value of l
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:
- Length = 500 ft
- Width = 30 ft
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