Evaluate and compare the ratios of corresponding sides.
B
b
Notice that the ratio of areas is equal to the squared scale factor.
A
a
See solution.
B
b
18 bottles
Practice makes perfect
a
We are asked to explain why the actual sign is a dilation of Aimee's sample. To do this, let's evaluate the ratio of widths and the ratio of lengths. We will start with converting the lengths given in feet to inches.
3&feet=3*12inches=36inches
7& 12feet=7 12*12inches=90inches
Using these values, we can evaluate the ratio of widths and the ratio of lengths.
Width of the actual sign/Width of the sample=36/6=6
Length of the actual sign/Length of the sample=90/15=6
Since the ratio of widths is the same as the ratio of lengths, the actual sign is a dilation of Aimee's sample.
b
We know that Aimee used 12 a bottle of glass paint to paint her sample, and we are asked to find the number of bottles Aimee will need to complete the actual sign. Let A represent the area, and L and W represent the length and width.
A_(sign)/A_(sample)=L_(sign)*W_(sign)/L_(sample)*W_(sample)
Since each dimension of the actual sign is 6 times the dimension of the sample, the area of the actual sign will be 6*6=36 times the area of the sample. This means that Aimee will need 36 times more bottles of glass paint to complete the actual sign.
1/2*36=18
Aimee will need 18 bottles of glass paint to complete the actual sign.
