a determined gardener has 100 ft of deer-resistant fence. she wants to enclose a rectangular vegetable garden in her backyard, and she wants the area that is enclosed to be at least 600 ft2. what range of values (in ft) is possible for the length of her garden? (enter your answer using interval notation.)

With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object.
A rectangle's opposing sides are equal and parallel.
Rectangles are two-dimensional shapes, and as such, they have length and width as their defining characteristics.

The garden is to be rectangular shape.

Let x = width

Let y = length

Set the equations for perimeter and area.

2(x + y) = 100 -----> perimeter

x + y = 50 ------> perimeter

xy = 600 ----> area

We have two equations to work with.

x + y = 50 eq1

xy = 600 eq2

Substitute eq1 into eq2. We can get eq2 in terms of x.

x(50 - x) = 600

-x2 + 50x = 600

-x2 + 50x - 600 = 0

Divide both sides of the equation by -1, so that we have a positive x2. The goal is to try to use FOIL to factor.

x2 - 50x + 600 = 0

(x - 30)(x - 20) = 0

x = 30 and x = 20

Next, we plug in these values of x into eq1 to solve for y.

y = 50 - x and y = 50 - x

y = 50 - 30 y = 50 - 20

y = 20 y = 30

Based on this, the range of values for the length is

20 ≤ y ≤ 30

Learn more about Rectangles

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