A rectangular field is enclosed by 360 feet of fencing. What is the length, in feet, of the field if it’s length is 6 feet more
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Answer:
Step-by-step explanation:
The date from the given table, is expressed as follows;
Area of Vegetable Garden (in square feet); 338, ___, 147.25, ___
Length of Tomato Patch (in feet); ___, 6.5, ___, 7
The length of the tomato patch increases with decrease in the area of the garden
Given that the length of the tomato patch is the independent variable, we can have;
Length of Tomato Patch (in feet); 6.25, 6.5, 6.75, 7
Therefore, for an increase in the length of the tomato patch from 6.25 to 6.75, (a change of Δl = 0.5) the area of the vegetable garden decreased from 338 to 147.25 which is a decrease of ΔA = 190.75
Therefore, the width of the tomato patch, w = ΔA/Δl = 190.75/0.5 = 381.5
The width of the tomato patch, w = 381.5 ft.
The relationship between the total area, TA, the area of the vegetable garden, <em>A</em>, and the length of the tomato patch, <em>l</em>, is therefore, given as follows;
A = TA - 381.5·l
338 = TA - 381.5×6.25
TA = 338 + 381.5×6.25 = 2,722.375
Therefore, when l = 6.5, we get
A = 2,722.375 - 381.5×6.5 = 242.625
When l = 7, we get
A = 2,722.375 - 381.5×7 = 51.875
Therefore, we get;