Question

the square below is dilated by a scale factor of 5. 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 1 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: Calculate the perimeter of the original square

The formula for the perimeter of a square is \(P = 4s\), where \(s\) is the side - length. Given \(s = 9\), then \(P=4\times9 = 36\) units.

Step2: Calculate the area of the original square

The formula for the area of a square is \(A=s^{2}\). Given \(s = 9\), then \(A = 9^{2}=81\) units².

Step3: Calculate the perimeter of the dilated square

When a figure is dilated by a scale factor \(k\), the perimeter of the new figure \(P'\) is related to the perimeter of the original figure \(P\) by the formula \(P'=kP\). Here \(k = 5\) and \(P = 36\), so \(P'=5\times36=180\) units.

Step4: Calculate the area of the dilated square

When a figure is dilated by a scale factor \(k\), the area of the new figure \(A'\) is related to the area of the original figure \(A\) by the formula \(A'=k^{2}A\). Here \(k = 5\) and \(A = 81\), so \(A'=5^{2}\times81=25\times81 = 2025\) units².

Answer:

Perimeter of given square: \(36\) units; Area of given square: \(81\) units²; Perimeter of dilated square: \(180\) units; Area of dilated square: \(2025\) units².