Unit 1: Day 8

Day 8: Scale factor of sides and Scale factor of area

This lesson reflects what was taught about similar triangles, but can be applied to all shapes. 

Let's start with a simple example. To find out the scale factor from the smaller rectangle to the larger rectangle, you take 2 corresponding sides and put them in a ratio. For this the 2 ratios would be 20:24 and 10:12. Simplify both ratios and you get 5:6, and 5:6. This means that they are similar and he scale factor is 5/6. So, if all you had was the large rectangle, you could multiply is by 5/6 and get the small rectangle. 

Another example: 

The maker of the this picture took the ratios of 6:9 and 8:12. The resulting ratio is 2:3. they got 2/3 because a ratio is the same as a fraction, and 1.5 because that's 9 divided by 6.

 

Scale factor of area is a bit more complicated. Lets take this as an example:

The area of the rectangle now is 10 cm². If we take a scale factor of 2, the dimensions become 10cm by 4cm, or 40 cm². Even though each side was multiplied by 2, the area was increased 4 times. With a factor of 3, it would be 15 cm by 6cm, but the area would be 90 cm². Overall, whatever the scale factor is, square it. Volume is the same, but cube the dimension instead.

 

 

Just another example of how scale factor works!

Quiz Time!

1. If I increase this by a scale factor of 2, what is the area?

2. What is the simplified side ratio of the heights of the horses?

3. What is the length of  both the unknown lenths given the shapes are similar?

Just another example of how the scale factor works with

 

 

Key:

 

 

1. The original area is 36 cm², so using the scale factor of area, we double the dimensions. That would be 18 cm and 8 cm. This is 144 cm², or 4 times the area of the original shape.

 

 

2. First you have to convert the heights to the same unit. I did 5 x 12 so that the bigger horse would be in inches. The fraction is 5/60. Simplified, this is 1/12.

 

 

3. The missing length EF is 6.5 cm, and the missing length AB is 5 cm. I found that because our 6:12 ratio, the only one we're given, tells us that the smaller one is half the size of the larger. one.