Find the scale factor that takes rectangle ABCD to rectangle EFGH.
2.25
Practice makes perfect
Let's draw the similar rectangles, one with a side AB=4 and another with corresponding side EF=6. To work with the areas, we need to know two adjacent sides of the rectangles. Therefore, to get the adjacent side of rectangle ABCD we can use an arbitrary value and let AD=a.
If we are going to compare the areas to determine how much larger rectangle EFGH is, we need to express EH in terms of a as well. To do this, we need to find the scale factor.
Scale Factor: r=AB/EH=6/4=1.5
With this scale factor, we know that EH=1.5a. This also means that we can find the areas of the two rectangles.
Now let's look at the ratio of the areas of the rectangles.
Therefore, rectangle EFGH is 2.25 times larger than rectangle ABCD.
Alternative Solution
Using Ratios of Similarity
When looking at different dimensions of similar figures, we need to adjust the ratio to the type of measurement.
Measurement
Ratio
Length
a:b
Area
a^2:b^2
Volume
a^3:b^3
Notice that we are given a unit of length for each of two similar rectangles. Let's fill those values into our table using the larger rectangle's length first. We need to find the ratio for the area.
Measurement
Ratio
a=6 and b=4
Length
a:b
6:4
Area
a^2:b^2
6^2:4^2
Recall ratios are fractions. Let's simplify the ratio to get our multiplier.
