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: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width.

Step2: Calculate perimeter of first rectangle

For the first rectangle with length $4x + 5$ and width $2x+7$, $P_1=2((4x + 5)+(2x + 7))=2(6x + 12)=12x+24$.

Step3: Calculate perimeter of second rectangle

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

Step4: Calculate combined perimeter

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

Answer:

E. $24x + 52$