Calculating Areas and Perimeters of Special Right Triangles

This video tutorial covers special right triangles, focusing on 45-45-90 and 30-60-90 triangles. It explains the unique relationships between the sides and hypotenuse of these triangles, using the Pythagorean theorem to solve for missing sides. The tutorial provides detailed examples and practice problems to reinforce understanding of these concepts.

What is the hypotenuse of a 45-45-90 triangle if one leg is 5?

• 5

• 5√2

• 10

• 25

How do you find the leg of a 45-45-90 triangle from the hypotenuse?

• Multiply by 2

• Divide by 2

• Divide by √2

• Multiply by √2

In a 45-45-90 triangle, if the hypotenuse is 5√2, what is the length of one leg?

• 2.5

• 10

• 5

• 5√2

In a 30-60-90 triangle, how is the hypotenuse related to the shortest side?

• Three times the length

• Half the length

• Equal to the length

• Twice the length

What is the length of the longer leg in a 30-60-90 triangle if the shorter leg is 4?

• 4√3

• 8

• 2√3

• 4√2

How do you rationalize the denominator when dividing by √3?

• Divide by √3

• Multiply by √2/√2

• Divide by √2

• Multiply by √3/√3

For a 30-60-90 triangle, if the longer leg is 4√3, what is the length of the hypotenuse?

• 8√3

• 8

• 4

• 2√3

If the shorter leg of a 30-60-90 triangle is 2, what is the length of the longer leg?

• 4

• 2

• 2√2

• 2√3

What is the perimeter of an equilateral triangle with a side length of 4√3?

• 12

• 8√3

• 12√3

• 24

What is the area of a rectangle formed by joining two 30-60-90 triangles with a hypotenuse of 4?

• 8√3 units squared

• 24 units squared

• 16 units squared

• 32√3 units squared