Question

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. rectangle a 2 cm 8.7 cm part a do you agree or disagree with lily? explain your answer.

Explanation:

Step1: Recall area - scale - factor relationship

When the scale factor for lengths is $k$, the scale - factor for areas is $k^{2}$.

Step2: Identify the given scale factor

The given scale factor for lengths $k = 2.5$.

Step3: Calculate the scale factor for areas

The scale factor for areas is $k^{2}=2.5^{2}=6.25$.

Step4: Analyze Lily's claim

Lily claims the area of the scale - drawing is 2.5 times the area of rectangle A. But the correct factor is 6.25 times. So, her claim is incorrect.

Answer:

Disagree. When the scale factor for lengths is 2.5, the scale factor for areas is $2.5^{2}=6.25$, not 2.5.