Question

select the correct answer. if the side length of square a is 12 times the side length of square b, which statement is true? the perimeter of square a is 144 times the perimeter of square b. the perimeter of square a is 12 times the perimeter of square b. the perimeter of square a is 48 times the perimeter of square b. the perimeter of square a is 6 times the perimeter of square b.

Explanation:

Step1: Recall perimeter formula for square

The perimeter of a square $P = 4s$, where $s$ is the side - length of the square. Let the side - length of square B be $s_B$ and that of square A be $s_A$. Given $s_A=12s_B$.

Step2: Calculate perimeters of squares A and B

The perimeter of square B, $P_B = 4s_B$. The perimeter of square A, $P_A=4s_A$. Substitute $s_A = 12s_B$ into the formula for $P_A$, we get $P_A=4\times(12s_B)=48s_B$.

Step3: Find the ratio of perimeters

$\frac{P_A}{P_B}=\frac{48s_B}{4s_B}=12$. So $P_A = 12P_B$.

Answer:

The perimeter of square A is 12 times the perimeter of square B.