Question:
Miriam is making a bulletin board that is shaped like a square. She has 72 inches of border material. If x represents the length of one side of the bulletin board, which inequality model and solution set best represents the possible side lengths of Miriam's bulletin board?
Answer:
[tex]x \le 18[/tex]
Step-by-step explanation:
Given
[tex]Border\ Material = 72[/tex]
Required
Determine an inequality for x
Represent the side lengths of the border with y. So:
Since the border is on the 4 sides, then
[tex]4y = 72[/tex] -- i.e. the perimeter of the border material
Solve for y
[tex]y =\frac{72}{4}[/tex]
[tex]y =18[/tex]
Recall that x represents the board's side length.
Since x will be situated inside the boarder, then.
[tex]x \le y[/tex]
Substitute [tex]y =18[/tex]
[tex]x \le 18[/tex]
