Proportions and Similar Triangles

This video tutorial covers solving various application problems using proportions. It includes examples such as calculating medicine dosage based on body weight, estimating deer population using tagging techniques, determining travel time between cities, finding missing sides in similar triangles, and estimating the height of a flagpole using shadow lengths. Each example demonstrates the use of proportions to solve real-world problems.

If a person weighs 160 pounds, how much medicine should they take according to the given proportion?

• 45 milligrams

• 35 milligrams

• 50 milligrams

• 40 milligrams

If a person weighing 180 pounds needs to take medicine, how many milligrams should they take?

• 55 milligrams

• 50 milligrams

• 45 milligrams

• 40 milligrams

What is the estimated total deer population if 10 out of 50 caught deer are tagged?

• 500

• 400

• 600

• 700

How many deer are estimated if 12 out of 60 caught deer are tagged?

• 720

• 480

• 600

• 500

If you travel 600 miles in 3 days, how many total days will it take to travel 1200 miles?

• 4 days

• 5 days

• 7 days

• 6 days

If you travel 300 miles in 1.5 days, how many days will it take to travel 900 miles?

• 3 days

• 4.5 days

• 6 days

• 5 days

In similar triangles, if one side of the larger triangle is 20 and the corresponding side of the smaller triangle is 5, what is the ratio of the larger triangle to the smaller triangle?

• 5:1

• 4:1

• 1:4

• 1:5

In similar triangles, if the ratio of the sides is 3:1, what is the length of the missing side if the corresponding side in the larger triangle is 9?

• 6

• 3

• 12

• 9

If a yardstick casts a shadow of 3 feet and a flagpole casts a shadow of 30 feet, how tall is the flagpole?

• 30 feet

• 45 feet

• 40 feet

• 35 feet

What is the correct proportion to find the height of a flagpole if a 4-foot stick casts a 2-foot shadow and the flagpole casts a 20-foot shadow?

• 4/20 = x/2

• 2/4 = x/20

• 4/2 = x/20

• 2/20 = x/4