Question

A gardener wants to fence in her plot in two equal rectangular sections. If she has 54 yards of fence and the area of the entire plot is 108 square yards, find the possible dimensions of the garden.

Answer 1

Considering the perimeter and the area of the rectangle, the possible dimensions are of 22.11 yards and 4.89 yards.

What are the area and the perimeter of a rectangle?

Considering a perimeter of length l and width w, we have that:

• The area is lw.

• The perimeter is 2(l + w).

In this problem, considering the amount of fencing as the perimeter, and the area, we have that:

• 2(l + w) = 54 -> l + w = 27 -> w = 27 - l.

• lw = 108.

Then:

l(27 - l) = 108

l² - 27l + 108 = 0.

Which is a quadratic equation with coefficients a = 1, b = -27, c = 108, then:

$\Delta = b^2 - 4ac = (-27)^2 - 4(1)(108) = 297$

$x_1 = \frac{27 + \sqrt{297}}{2} = 22.11$

$x_2 = \frac{27 - \sqrt{297}}{2} = 4.89$

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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