Question

the rectangle below is dilated by a scale factor of 4. find the perimeter and area of the rectangle below, as well as the perimeter and area of the dilated rectangle. 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 rectangle units
area of given rectangle units²
perimeter of dilated rectangle units
area of dilated rectangle units²

Explanation:

Step1: Calculate the perimeter and area of the original rectangle

• Perimeter formula: \(P = 2(l + w)\), where \(l = 10\) and \(w=8\).

\(P=2(10 + 8)=2\times18 = 36\) units.

• Area formula: \(A=l\times w\).

\(A = 10\times8=80\) units².

Step2: Use the properties of dilation

• Perimeter of dilated figure: If a figure is dilated by a scale factor \(k\), the perimeter of the new figure \(P'\) is \(P'=k\times P\). Here \(k = 4\), so \(P'=4\times36 = 144\) units.
• Area of dilated figure: If a figure is dilated by a scale factor \(k\), the area of the new figure \(A'\) is \(A'=k^{2}\times A\). Here \(k = 4\), so \(A'=4^{2}\times80=16\times80 = 1280\) units².

Answer:

Perimeter of given rectangle: \(36\) units.
Area of given rectangle: \(80\) units².
Perimeter of dilated rectangle: \(144\) units.
Area of dilated rectangle: \(1280\) units².