Question

problems 5 - 6: ivory created a scaled copy of rectangle a. the area of ivory’s scaled copy is 48 square units. 5. how many times greater is the area of ivory’s scaled copy than the area of rectangle a? 6. what scale factor did ivory use to create the scaled copy? show or explain your thinking.

Explanation:

Step1: Find area of rectangle A

Rectangle A has length 2 units and width 1 unit. Area of rectangle A, $A_{A}=2\times1 = 2$ square - units.

Step2: Find ratio of areas

To find how many times greater the area of the scaled - copy is than the area of rectangle A, we divide the area of the scaled - copy by the area of rectangle A. Let $k$ be the ratio. $k=\frac{48}{2}=24$.

Step3: Recall relationship between area ratio and scale factor

If the scale factor is $s$, the ratio of the areas of two similar figures is $s^{2}$. We know the ratio of the areas of the scaled - copy to rectangle A is 24, so $s^{2}=24$, and $s = \sqrt{24}=2\sqrt{6}$.

Answer:

1. 24 times
2. $2\sqrt{6}$