Let's address the questions shown in your image one by one.

Question 1:

1. Formula for the area of a rectangle: $A = L \cdot W$

   • Units for $A$: If both $L$ (length) and $W$ (width) are measured in feet, the area $A$ will be in square feet because area is measured in two-dimensional space. Thus, the units for $A$ are square feet (ft²).

2. Solve the formula for $L$: Rearranging the equation $A = L \cdot W$ to solve for $L$: $L = \frac{A}{W}$ This means $L$ is the area divided by the width.

3. Area of a rectangle with given length and width:

   • Length $L = 14$ feet
   • Width $W = 9$ inches

   Since the width is given in inches, first convert it to feet. There are 12 inches in 1 foot, so: $W = \frac{9}{12} = 0.75 \text{ feet}$ Now, calculate the area: $A = L \cdot W = 14 \cdot 0.75 = 10.5 \text{ square feet (ft²)}$

Question 2:

1. Formula for the perimeter of a rectangle: $P = 2L + 2W$

   • Units for $P$: Perimeter is a one-dimensional measurement, so if both $L$ and $W$ are in feet, the perimeter $P$ will be in feet (ft).

2. Solve the formula for $L$: To solve for $L$, start from the formula for the perimeter: $P = 2L + 2W$ Isolate $L$ by subtracting $2W$ from both sides: $P - 2W = 2L$ Now, divide by 2 to solve for $L$: $L = \frac{P - 2W}{2}$

Would you like more detailed explanations or help with additional steps? Here are five related questions to expand on this topic:

1. How do you convert other units, such as meters to feet, in area or perimeter problems?
2. What is the difference between calculating perimeter and area for a rectangle?
3. How does changing the dimensions of a rectangle affect its area and perimeter?
4. Can you apply the same formulas for irregular shapes, or do they only work for rectangles?
5. How do you solve for $W$ in the formulas for area and perimeter if given other values?

Tip: Always ensure that units are consistent (e.g., both length and width should be in the same units before calculating area or perimeter).