Garden Perimeter and Width Inequalities

The video tutorial explains how to determine the range of possible widths for a rectangular garden with a fixed length of 12 feet, given that the perimeter must be between 36 and 48 feet. The instructor sets up a compound inequality using the perimeter formula, solves for the width, and concludes that the width must be between 6 and 12 feet.

What is the length of Liz's rectangular garden?

• 14 feet

• 16 feet

• 10 feet

• 12 feet

What is the minimum perimeter required for Liz's garden?

• 24 feet

• 30 feet

• 36 feet

• 42 feet

What is the maximum perimeter allowed for Liz's garden?

• 52 feet

• 44 feet

• 40 feet

• 48 feet

What type of inequality is used to express the perimeter constraints?

• Simple inequality

• Compound inequality

• Quadratic inequality

• Linear inequality

Which formula is used to calculate the perimeter of a rectangle?

• 2(l + w)

• 2l + 2w

• l + w

• l * w

What is the first step in setting up the compound inequality for the garden's perimeter?

• Find the diagonal

• Substitute the length

• Calculate the area

• Substitute the width

What is the value of 2 times the length of the garden?

• 26

• 24

• 22

• 20

What is the inequality for the minimum perimeter after substituting the length?

• 2w + 24 ≥ 36

• 2w + 24 ≤ 36

• 2w + 24 = 36

• 2w + 24 > 36

What is the inequality for the maximum perimeter after substituting the length?

• 2w + 24 ≤ 48

• 2w + 24 > 48

• 2w + 24 ≥ 48

• 2w + 24 = 48

What is the next step after setting up the inequalities to find the width?

• Subtract 24 from both sides

• Add 24 to both sides

• Divide both sides by 2

• Multiply both sides by 2