Question

Emily is creating a rectangular garden in her backyard. The length of the garden is 12 feet. The perimeter of the garden must be at least 30 feet and no more than 64 feet. Use a compound inequality to find the range of values for the width w of the garden.

Answer 1

The range of values for the width of the garden is 3 to 20 feet.

Step-by-step explanation:

To find the range of values for the width of the garden, we can use a compound inequality. The perimeter of a rectangle is calculated by adding twice the length with twice the width. So, the compound inequality for the perimeter is:

30 ≤ 2(12) + 2w ≤ 64

Simplifying the inequality, we get:

30 ≤ 24 + 2w ≤ 64

Subtracting 24 from all parts of the inequality:

6 ≤ 2w ≤ 40

Dividing all parts by 2, we get:

3 ≤ w ≤ 20

So, the range of values for the width of the garden is 3 to 20 feet.

Answer 2

The compound inequality:

30 ≤ 2L + 2w ≤ 64

w < 12

The range:

3 ≤ w < 12

Step-by-step explanation:

Let L be he length , w the width and p the perimeter

p=2L + 2w

30 ≤ p ≤ 64 ⇌ 30 ≤ 2L + 2w ≤ 64 ⇌ 30 ≤ 24 + 2w ≤ 64 ⇌ 6 ≤ 2w ≤ 40

⇌ 3 ≤ w ≤ 20

but ,since the width is less than the length then w < 12

then 3 ≤ w < 12