A local citizen wants to fence a rectangular community garden. The lengthof the garden should be at least 110ft., and the distance around should be no more than 380 ft. Write a system of inequalities that models the possible demensiopns of the garden. Graph the system to show all possible solutions.
To write a system of inequalities that models the possible dimensions of the garden, let's consider the length and width of the rectangular community garden.
Let's assume the length of the garden is "L" and the width is "W". We know that the length should be at least 110 ft, so we can write the inequality:
L ≥ 110
The distance around the garden is the perimeter, which is given as no more than 380 ft. The perimeter of a rectangle is calculated by adding the lengths of all sides, so we can write this inequality:
2L + 2W ≤ 380
Now, let's graph the system of inequalities to visualize the possible solutions.
1. Graph the equation L = 110. This is a vertical line that starts at the point (110, 0) and goes upward infinitely.
2. Graph the equation 2L + 2W = 380 by rearranging it to W = (380 - 2L)/2. This equation represents a line that connects two points: (0, 190) and (190, 0).
3. Shade the region that satisfies both inequalities. You'll shade the region to the right of the vertical line L = 110 and below the slanted line W = (380 - 2L)/2.
The shaded region represents all the possible solutions for the dimensions of the rectangular community garden.
Note: It is important to show the graph to find the exact solution.