Question

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

Answer 1

Part A

`A_(t)=22(12+w)`

Applying Distributive property:
`A_(t)=264+22w`

Part B

`A_(t)=660\ ft^2`

Explanation:

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

The formula for calculate the area of a rectangle is:

`A=lw`

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

Part A

Notice that the dimensions of the new bathroom are:

`l=22\ ft\\w=12\ ft`

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:

`A_(t)=22(12+w)`

Applying Distributive property:

`A_(t)=264+22w`

Part B

If the width of the bedroom is 18 feet, you need to substitute this value into the expression
`A_(t)=264+22w` in order to find the total square footage of the two rooms:

`A_(t)=264+22w\\\\A_(t)=660\ ft^2`