Question

question
the square below is dilated by a scale factor of 1/5. 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
perimeter of given square units
area of given square units²
perimeter of dilated square units
area of dilated square units²

Explanation:

Step1: Calculate perimeter of given square

Perimeter of a square \(P = 4s\) (where \(s\) is side - length). Given \(s = 45\) units. So \(P=4\times45 = 180\) units.

Step2: Calculate area of given square

Area of a square \(A=s^{2}\). Given \(s = 45\) units. So \(A = 45^{2}=2025\) units².

Step3: Find side - length of dilated square

If the scale factor is \(k=\frac{1}{5}\), and the original side - length \(s = 45\) units, then the new side - length \(s'=k\times s=\frac{1}{5}\times45 = 9\) units.

Step4: Calculate perimeter of dilated square

Using the perimeter formula \(P'=4s'\). Substitute \(s' = 9\) units. So \(P'=4\times9=36\) units.

Step5: Calculate area of dilated square

Using the area formula \(A'=(s')^{2}\). Substitute \(s' = 9\) units. So \(A'=9^{2}=81\) units².

Answer:

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