Question

what is the combined perimeter of these two rectangles? a 6x + 14 b 12x + 24 c 12x + 26 d 15x + 31 e 24x + 52

Explanation:

Step1: Find perimeter of first rectangle

The formula for the perimeter of a rectangle is $P = 2(l + w)$. For the first rectangle with length $4x + 5$ and width $2x+7$, we have $P_1=2((4x + 5)+(2x + 7))=2(6x+12)=12x + 24$.

Step2: Find perimeter of second rectangle

For the second rectangle with length $3x + 14$ and width $3x$, we have $P_2=2((3x + 14)+3x)=2(6x + 14)=12x+28$.

Step3: Find combined perimeter

$P = P_1+P_2=(12x + 24)+(12x+28)=24x + 52$.

Answer:

E. $24x + 52$