Questions: Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, I, and the possible width, w, that her frame could have? I ≤ 12 2l+2w<30 I ≤ 12 l+w<30

Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, I, and the possible width, w, that her frame could have?

I ≤ 12
2l+2w<30

I ≤ 12
l+w<30

Transcript text: Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, $I$, and the possible width, $w$, that her frame could have? \[ I \leq 12 \] $2 l+2 w<30$ \[ I \leq 12 \] \[ I+w<30 \]

Solution

Solution Steps

Step 1: Identify the Constraints

The length of the frame, $ l $, must be no more than 12 inches. This gives us the inequality: \[ l \leq 12 \]

Step 2: Formulate the Perimeter Inequality

Marisol has less than 30 inches of wood to use for the perimeter of the frame. The perimeter of a rectangle is given by $ 2l + 2w $. Therefore, the inequality for the perimeter is: \[ 2l + 2w < 30 \]

Step 3: Simplify the Perimeter Inequality