Write an expression for the total area of both rooms by multiplying their common width by their combined length, one room is 15 by 20 feet and the other is 15 by ?

The total area of both rooms can be found by multiplying their common width by their combined length. Let's define the dimensions:

- First room: \( 15 \, \text{ft} \times 20 \, \text{ft} \)
- Second room: \( 15 \, \text{ft} \times x \, \text{ft} \) (where \( x \) is the unknown length)

Both rooms share the common width of 15 feet. So, to find the total area, we multiply this common width by the combined length of the two rooms.

The combined length is \( 20 + x \) feet.

Thus, the total area \( A \) is given by the expression:
\[
A = 15 \times (20 + x)
\]

This can be simplified as:
\[
A = 15(20 + x) = 15 \times 20 + 15 \times x = 300 + 15x
\]

So, the expression for the total area is:
\[
A = 300 + 15x \, \text{square feet}.
\]

Would you like further details on this or any other questions?

Here are 5 related questions for further exploration:
1. How would the expression change if the width of one of the rooms was different?
2. What is the total area if the second room’s length is 10 feet?
3. How can we express the perimeter of both rooms combined?
4. What happens to the total area if the width is doubled but the lengths stay the same?
5. How can we calculate the area for irregular-shaped rooms?

**Tip:** When dealing with areas, always ensure that the units are consistent throughout the calculation.

Calculate the total area of two rooms by using their common width and combined length. One room measures 15 by 20 feet, while the second room's length is unknown. Learn how to express the total area using basic algebra and geometry, suitable for students in Grades 6-8.

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