Question

A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft, and the distance around should be no more than 380 ft. Write a system of inequalities that models the possible dimensions of the garden. Graph the system to show all possible solutions.

a. Length ≥ 110 ft
b. 2(Length + Width) ≤ 380 ft
c. Width ≥ 0
d. Length × Width ≥ 0

Answer 1

A graph of the system of inequalities that models the possible dimensions of the garden is shown in the image below.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = xy

Where:

• A represent the area of a rectangle.
• x represent the width of a rectangle.
• y represent the length of a rectangle.

Based on the information provided above, a system of inequalities that models the situation can be written as follows;

x ≥ 110 ft

2(x + y) ≤ 380 ft

y ≥ 0

xy ≥ 0

In conclusion, a possible solution is (150, 20), which means a length of 150 feet and width of 20 feet.