Question

The length of a living room is 12 feet and its width is 1012 feet. The length of the room is being expanded by x feet. Choose an expression to represent the new area of the living room in square feet and the expanded form of the expression. Select all that apply.

A. 10.5(12x) square feet
B. (10.5 + 12 + x) square feet
C. 10.5(12 + x) square feet
D. 126x square feet
E. (126 + 10.5x) square feet
F. (22.5 + x) square feet

Answer 1

Option C. 10.5(12 + x) square feet

Option E. (126 + 10.5x) square feet

Explanation:

step 1

Find the area of the original living room

we know that

The area of the original living room is equal to

`A=LW`

we have

`L=12\ ft\\W=10(1)/(2)\ ft=10.5\ ft`

substitute

`A=(12)(10.5)=126\ ft^2`

step 2

Find the new area of the living room

The length of the room is being expanded by x feet

so

we have

`L=(12+x)\ ft\\W=10.5\ ft`

The new area is

`A=10.5(12+x)\ ft^2`

The expanded form of the expression is

Apply distributive property

`A=10.5(12)+10.5(x)\\A=(126+10.5x)\ ft^2`