Question

question
the rectangle below is dilated by a scale factor of 2. 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 perimeter of given rectangle

Perimeter formula for rectangle \(P = 2(l + w)\). Here \(l = 22\), \(w = 16\).
\(P=2(22 + 16)=2\times38 = 76\) units.

Step2: Calculate area of given rectangle

Area formula for rectangle \(A=l\times w\). Here \(l = 22\), \(w = 16\).
\(A = 22\times16=352\) units².

Step3: Calculate perimeter of dilated rectangle

When a figure is dilated by scale factor \(k\), new perimeter \(P_{new}=k\times P_{old}\). Here \(k = 2\), \(P_{old}=76\).
\(P_{new}=2\times76 = 152\) units.

Step4: Calculate area of dilated rectangle

When a figure is dilated by scale factor \(k\), new area \(A_{new}=k^{2}\times A_{old}\). Here \(k = 2\), \(A_{old}=352\).
\(A_{new}=2^{2}\times352=4\times352 = 1408\) units².

Answer:

Perimeter of given rectangle: \(76\) units.
Area of given rectangle: \(352\) units².
Perimeter of dilated rectangle: \(152\) units.
Area of dilated rectangle: \(1408\) units².