The haynes family is building an addition to their house that includes a new
bedroom and a new bathroom. both rooms will have the same length. mr.
haynes created a model on a piece of paper as shown below:
22 feet

new bathroom
12 feet
new bedroom w
part a: write an expression for the total area of both rooms by using the distributive property.
part b: if the width of the bedroom is 18 feet, what is the total square footage of the two room

Part A

Applying Distributive property:

Part B

Step-by-step explanation:

Attached is the model that belongs to this exercise (The model was missing)

The formula for calculate the area of a rectangle is:

Where "l" is the lenght and "w" is the width.

Part A

Notice that the dimensions of the new bathroom are:

We do not know the width of the new bathroom, but we know that both rooms will have the same length. Knowing this, we can write an expression for the total area of both rooms by using the Distributive Property:

Applying Distributive property:

Part B

If the width of the bedroom is 18 feet, you need to substitute this value into the expression in order to find the total square footage of the two rooms:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x