Equilateral Triangle Properties and Ratios

The video tutorial explains how to determine the perimeter of an equilateral triangle given its height. It uses the properties of a 30-60-90 triangle, where the sides are in a constant ratio of 1, 2, and √3. By multiplying these sides by a variable x, the video demonstrates how to solve for x using the given height. The example problem shows that the height divides the equilateral triangle into two 30-60-90 triangles, allowing for the calculation of side lengths and ultimately the perimeter. The tutorial concludes with a perimeter calculation of 36 units.

What is the main goal of the example discussed in the video?

• To find the area of a square

• To determine the perimeter of an equilateral triangle

• To measure the circumference of a circle

• To calculate the volume of a cube

What are the typical side ratios of a 30, 60, 90 triangle?

• 1, 1, 1

• 1, √2, √3

• 1, 2, 3

• 1, 2, √3

How can the sides of a 30, 60, 90 triangle be scaled?

• By multiplying each side by a constant

• By adding a constant to each side

• By subtracting a constant from each side

• By dividing each side by a constant

What is the given height of the equilateral triangle in the example?

• 6√3

• 12

• 6

• 12√3

Into how many 30, 60, 90 triangles is the equilateral triangle divided?

• Two

• Four

• Three

• One

What is the length of the longer leg of the 30, 60, 90 triangle in the example?

• 12

• 6√3

• 6

• 12√3

What is the value of X when solving for the side lengths of the equilateral triangle?

• 9

• 12

• 6

• 3

What is the length of each side of the equilateral triangle?

• 6 units

• 9 units

• 12 units

• 15 units

How do you calculate the perimeter of the equilateral triangle?

• Subtract the length of one side from the sum of the other two

• Multiply the length of one side by 3

• Multiply the length of one side by 2

• Add the lengths of all three sides

What is the final perimeter of the equilateral triangle?

• 42 units

• 36 units

• 30 units

• 24 units