Question

the rectangle below is dilated by a scale factor of \\(\frac{1}{5}\\). 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.

35
25

answer attempt 1 out of 2

perimeter of given rectangle \\(\square\\) units perimeter of dilated rectangle \\(\square\\) units
area of given rectangle \\(\square\\) units\\(^2\\) area of dilated rectangle \\(\square\\) units\\(^2\\)

Explanation:

Step1: Calculate perimeter of given rectangle

Perimeter formula for rectangle \(P = 2(l + w)\). Here \(l = 35\), \(w = 25\).
\(P=2(35 + 25)=2\times60 = 120\)

Step2: Calculate area of given rectangle

Area formula for rectangle \(A=l\times w\). Here \(l = 35\), \(w = 25\).
\(A = 35\times25=875\)

Step3: Find dimensions of dilated rectangle

Scale factor \(k=\frac{1}{5}\). New length \(l'=35\times\frac{1}{5}=7\), new width \(w'=25\times\frac{1}{5} = 5\)

Step4: Calculate perimeter of dilated rectangle

Using \(P = 2(l + w)\) with \(l' = 7\), \(w' = 5\)
\(P'=2(7 + 5)=2\times12 = 24\)

Step5: Calculate area of dilated rectangle

Using \(A=l\times w\) with \(l' = 7\), \(w' = 5\)
\(A'=7\times5 = 35\)

Answer:

Perimeter of given rectangle: \(120\) units
Area of given rectangle: \(875\) units²
Perimeter of dilated rectangle: \(24\) units
Area of dilated rectangle: \(35\) units²