Question

question: the square below is dilated by a scale factor of 4. 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. answer: attempt 2 out of 2 perimeter of given square units area of given square units² perimeter of dilated square units area of dilated square units²

Explanation:

Step1: Find perimeter of original square

The side - length of the original square is $s = 12$ units. The perimeter formula of a square is $P=4s$. So, $P_{original}=4\times12 = 48$ units.

Step2: Find area of original square

The area formula of a square is $A = s^{2}$. So, $A_{original}=12^{2}=144$ square units.

Step3: Find side - length of dilated square

When a figure is dilated by a scale factor $k = 4$, the new side - length $s_{new}=k\times s$. Here, $s_{new}=4\times12 = 48$ units.

Step4: Find perimeter of dilated square

Using the perimeter formula $P = 4s$, with $s = 48$ units, $P_{dilated}=4\times48=192$ units.

Step5: Find area of dilated square

Using the area formula $A=s^{2}$, with $s = 48$ units, $A_{dilated}=48^{2}=2304$ square units.

Answer:

Perimeter of given square: 48 units
Area of given square: 144 units²
Perimeter of dilated square: 192 units
Area of dilated square: 2304 units²