Considering the perimeter and the area of the rectangle, the possible dimensions are of 22.11 yards and 4.89 yards.
Considering a perimeter of length l and width w, we have that:
In this problem, considering the amount of fencing as the perimeter, and the area, we have that:
Then:
l(27 - l) = 108
l² - 27l + 108 = 0.
Which is a quadratic equation with coefficients a = 1, b = -27, c = 108, then:
[tex]\Delta = b^2 - 4ac = (-27)^2 - 4(1)(108) = 297[/tex]
[tex]x_1 = \frac{27 + \sqrt{297}}{2} = 22.11[/tex]
[tex]x_2 = \frac{27 - \sqrt{297}}{2} = 4.89[/tex]
Then, the possible dimensions are of 22.11 yards and 4.89 yards.
More can be learned about the perimeter and the area of a rectangle at https://brainly.com/question/10489198
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