Question

c. find another value of x that is a solution of both inequalities.

1. the maximum area that is available for a rectangular garden is 80 square feet.

a. write an inequality that represents the possible dimensions for the garden.
b. find three different sets of allowable dimensions for the garden. find the area of each garden.

Explanation:

Part a

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by \( A = l \times w \), where \( l \) is the length and \( w \) is the width.

Step2: Set up the inequality

Since the maximum area available is 80 square feet, the area of the rectangular garden ( \( l \times w \)) must be less than or equal to 80. So the inequality is \( lw \leq 80 \), where \( l>0 \) and \( w>0 \) (because length and width cannot be zero or negative).

Step1: Choose positive values for \( l \) and \( w \) such that \( lw \leq 80 \)

We can pick different pairs of positive numbers whose product is less than or equal to 80.

Step2: First set of dimensions

Let \( l = 10 \) feet and \( w = 8 \) feet. Then the area \( A = 10\times8 = 80 \) square feet (which satisfies \( 80\leq80 \)).

Step3: Second set of dimensions

Let \( l = 5 \) feet and \( w = 10 \) feet. Then the area \( A = 5\times10 = 50 \) square feet (and \( 50\leq80 \)).

Step4: Third set of dimensions

Let \( l = 20 \) feet and \( w = 3 \) feet. Then the area \( A = 20\times3 = 60 \) square feet (and \( 60\leq80 \)).

Answer:

The inequality is \( lw \leq 80 \) with \( l > 0 \) and \( w > 0 \) (where \( l \) is the length and \( w \) is the width of the garden).

Part b