The area of a rectangle is the amount of space it would cover on a 2-Dimensional plane. The required value of the width is 25 feet.
A rectangle is a plane shape with equal opposite sides. Its area can be determined by;
Area of a rectangle = length x width
Considering the given question, let the length of the plot be represented by l and its width as w. Given that the width of the plot should be longer than its length by 5, then we have;
w = l + 5
But,
Area of the plot = length x width
500 = l x (l + 5)
= [tex]l^{2}[/tex] + 5l
This implies that,
500 = [tex]l^{2}[/tex] + 5l
[tex]l^{2}[/tex] + 5l - 500 = 0
Applying the quadratic formula, we have;
l = (-b ± [tex]\sqrt{b^{2} - 4ac}[/tex]) / 2a
a = 1, b = 5, c = -500
= (-5 ± [tex]\sqrt{5^{2} - (4*1*-500)}[/tex]/ 2
= (-5 ± 45) / 2
l = (40) / 2 OR l = (-50) / 2
l = 20 OR l = - 25.5
So that,
l = 20
Therefore, the length of the plot is 20 feet.
Thus the width of the plot can be determined as;
w = l + 5
= 20 + 5
w = 25
The width of the plot is 25 feet.
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