Please show me how to set this up:
A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110ft., and the distance around should be no more than 380ft. Write a system of inequalities that models the possible dimensions of the garden.
L >= 110
P <= 380
Now, 2(W+L) = P
W+L <= 190
So,
L >= 110
W <= 80
To set up a system of inequalities that models the possible dimensions of the garden, we need to consider the given conditions:
1. The length of the garden should be at least 110ft.
2. The distance around the garden should be no more than 380ft.
Let's assume the length of the garden as 'L' and the width of the garden as 'W'.
Based on the conditions, we can write the following inequalities:
1. The length of the garden should be at least 110ft: L ≥ 110.
2. The distance around the garden should be no more than 380ft: 2L + 2W ≤ 380.
The equation 2L + 2W represents the perimeter of a rectangle, where 2L represents the sum of the lengths of the two opposite sides, and 2W represents the sum of the lengths of the other two opposite sides.
Therefore, the system of inequalities that models the possible dimensions of the garden is:
L ≥ 110,
2L + 2W ≤ 380.