Question

the square below is dilated by a scale factor of 2. find the perimeter and area of the square below, as well as the perimeter and area of the dilated square. express your answers 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 formula for the perimeter of a square is $P = 4s$, where $s$ is the side - length. Given $s = 3$, so $P_{1}=4\times3 = 12$ units.

Step2: Find area of given square

The formula for the area of a square is $A=s^{2}$. Given $s = 3$, so $A_{1}=3^{2}=9$ square units.

Step3: Find side - length of dilated square

The square is dilated by a scale factor of 2. If the original side - length is $s = 3$, the new side - length $s_{2}=2\times3 = 6$ units.

Step4: Find perimeter of dilated square

Using the perimeter formula $P = 4s$, with $s = 6$, we get $P_{2}=4\times6 = 24$ units.

Step5: Find area of dilated square

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

Answer:

Perimeter of given square: 12 units
Area of given square: 9 square units
Perimeter of dilated square: 24 units
Area of dilated square: 36 square units