Finding Height Using Proportions and Shadows

Proportion and Similarity Practice

November 12, 2020

Multiple Choice

Example 1, Part 1: 

A tree 24 feet tall casts a shadow 12 feet long. Brad is 6 feet tall. Which of the following is NOT a proportion that accurately represents the given example?

• $$\frac{24}{12}=\frac{6}{x}$$

• $$\frac{24}{6}=\frac{12}{x}$$

• $$\frac{24}{12}=\frac{x}{6}$$

Example 3

Copy down the diagram. You will be using it for the next two questions

Multiple Choice

Example 3, Part 1:

A girl 160 cm tall, stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. Which of the following is a proportion that accurately represents the given situation?

• $$\frac{x}{160}=\frac{360}{90}$$

• $$\frac{x}{160}=\frac{450}{90}$$

• $$\frac{x}{450}=\frac{90}{160}$$

Fill in the Blanks

Multiple Choice

True or False:

$$Ratio\ of\ sides=Ratio\ of\ the\ Perimeters$$  

• True

• False

Multiple Choice

True or False:

$$\left(Ratio\ of\ sides\right)^2=Ratio\ of\ the\ Areas$$  

• True

• False

Multiple Choice

Example 4, Part 1:
Triangles IJK and TUV are similar. The length of the sides of IJK are 40, 50, and 24. The length of the longest side of TUV is 275. Which of the following proportions can be used to solve for the perimeter of TUV?

• $$\frac{114}{x}=\frac{50}{275}$$  

• $$\frac{24}{x}=\frac{50}{275}$$  

Example 5

Copy down the diagram. You will be using it for the next question