A local citizen wants to fence a rectangular community garden. The length of the garden should at least be 110 ft. and the distance around should be no more than 380 ft. Which system of inequalities and graph represent the possible dimensions?
@damon pleaseee help!!!
perimeter = 2 w + 2 L </= 380
so
w + L </= 190
and
L >/= 110
I don't understand ??
@damon
the sum of the width and length can be no more than half of 380
the length must be at least 110
graph the line w = 190 - L
everything under and including that is shaded
graph the line L </= 110
it is horizontal or vertical depending on which axis you chose for width
everything left or under that is shaded
where the two shadings unite, that is your region.
Im still confused @damon i cant figure it out?
>110
<380
that easy
To determine the system of inequalities and graph that represent the possible dimensions of the community garden, we need to consider the given conditions.
Let's assume the length of the garden is represented by L and the width is represented by W.
According to the given conditions:
1. The length should be at least 110 ft: L ≥ 110
2. The distance around the garden should be no more than 380 ft: 2L + 2W ≤ 380
Therefore, the system of inequalities representing the possible dimensions of the garden is:
L ≥ 110
2L + 2W ≤ 380
To graphically represent this system of inequalities, we can plot the inequalities on a coordinate plane.
First, let's graph the line L = 110. This is a vertical line passing through the x-axis at x = 110.
Next, let's graph the inequality 2L + 2W ≤ 380. To do this, we can rearrange the inequality and plot the line 2L + 2W = 380, which is the boundary line of the shaded region.
To find two points on this line, we can assign arbitrary values for L and solve for W:
When L = 110, 2(110) + 2W = 380
220 + 2W = 380
2W = 160
W = 80
So, one point on the line is (110, 80).
When W = 0, 2L + 2(0) = 380
2L = 380
L = 190
So, another point on the line is (190, 0).
Plot these two points and draw a line passing through them. This line represents the inequality 2L + 2W ≤ 380.
The possible dimensions of the garden lie within or on the shaded region below or on this line.
I hope this explanation helps you understand how to represent the possible dimensions of the community garden using a system of inequalities and a graph.