Question

the square below is dilated by a scale factor of 3. find the perimeter and area of the square below, and the perimeter and area of the dilated square. express your answer as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). figures are not necessarily drawn to scale.

Explanation:

Step1: Find perimeter of given square

The side - length of the given square is $s = 2$. The perimeter formula for a square is $P=4s$. So, $P_{1}=4\times2 = 8$.

Step2: Find area of given square

The area formula for a square is $A = s^{2}$. So, $A_{1}=2^{2}=4$.

Step3: Find side - length of dilated square

The scale factor is $k = 3$. The side - length of the dilated square $s_{2}=k\times s=3\times2 = 6$.

Step4: Find perimeter of dilated square

Using the perimeter formula $P = 4s$, for the dilated square with $s = 6$, we have $P_{2}=4\times6=24$.

Step5: Find area of dilated square

Using the area formula $A = s^{2}$, for the dilated square with $s = 6$, we have $A_{2}=6^{2}=36$.

Answer:

Perimeter of given square: $8$
Area of given square: $4$
Perimeter of dilated square: $24$
Area of dilated square: $36$