Question

1. lily uses a scale factor of 2.5 to create a scale drawing of rectangle a. she claims that the area of her scale drawing is 2.5 times the area of rectangle a.

part a
do you agree or disagree with lily? explain your answer
part b
what is the area of lilys scale drawing?
_____ sq cm

Explanation:

Part A

Step1: Recall the scale - factor and area relationship

If the scale factor of two similar figures is \(k\), the ratio of their areas is \(k^{2}\). Here, the scale factor \(k = 2.5\).

Step2: Analyze Lily's claim

Lily claims that if the scale factor is \(k = 2.5\), the area of the scale - drawing is \(k=2.5\) times the area of rectangle \(A\). But the correct relationship is that the area of the scale - drawing should be \(k^{2}=(2.5)^{2}=6.25\) times the area of rectangle \(A\). So, we disagree with Lily.

Part B

Step1: Calculate the area of rectangle \(A\)

The area of rectangle \(A\), \(A_{A}=l\times w\), where \(l = 8.2\mathrm{cm}\) and \(w = 2\mathrm{cm}\). So, \(A_{A}=8.2\times2=16.4\mathrm{cm}^{2}\)

Step2: Calculate the area of the scale - drawing

Since the scale factor \(k = 2.5\), and the area of the scale - drawing \(A_{s}=k^{2}\times A_{A}\)
Substitute \(k = 2.5\) and \(A_{A}=16.4\) into the formula: \(A_{s}=(2.5)^{2}\times16.4\)
First, \((2.5)^{2}=6.25\)
Then, \(A_{s}=6.25\times16.4 = 102.5\mathrm{cm}^{2}\)

Answer:

Part A

Disagree. Because if the scale factor of two similar rectangles is \(k\), the ratio of their areas is \(k^{2}\). Here \(k = 2.5\), so the area of the scale - drawing should be \(2.5^{2}=6.25\) times the area of rectangle \(A\), not \(2.5\) times.

Part B

\(102.5\)