Question

the length of a living room is 12 feet and its width is 10\frac{1}{2} feet. the length of the room is being extended by x feet. which expression represents the area of the living room in square feet?\
a. 10.5(12) 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

Explanation:

Step1: Convert mixed number to decimal

$10\frac{1}{2} = 10.5$

Step2: Find new length

New length = $12 + x$

Step3: Calculate area formula

Area = width $\times$ new length = $10.5(12 + x)$

Step4: Expand the formula

$10.5(12 + x) = 10.5\times12 + 10.5x = 126 + 10.5x$

Answer:

C. $10.5(12 + x)$ square feet
E. $(126 + 10.5x)$ square feet