ACT SAT PREP How to determine the perimeter of a special right triangle

The video tutorial covers the properties and relationships of special right triangles, specifically 30-60-90 and 45-45-90 triangles. It explains how to use these properties to solve problems, including calculating the perimeter of a triangle. The tutorial emphasizes understanding the relationships between the sides of these triangles and provides a step-by-step approach to solving related problems.

What is the relationship between the short leg and the hypotenuse in a 30-60-90 triangle?

• The hypotenuse is equal to the short leg.

• The hypotenuse is twice the short leg.

• The hypotenuse is half the short leg.

• The hypotenuse is three times the short leg.

In a 45-45-90 triangle, what is the relationship between the legs and the hypotenuse?

• The hypotenuse is three times one of the legs.

• The hypotenuse is twice one of the legs.

• The hypotenuse is equal to one of the legs.

• The hypotenuse is the square root of 2 times one of the legs.

If the longer leg of a 30-60-90 triangle is 12 inches, what is the length of the short leg?

• 12 times the square root of 3

• 12 divided by the square root of 3

• 6 inches

• 12 inches

How do you find the hypotenuse of a 30-60-90 triangle if the short leg is known?

• Multiply the short leg by 3

• Multiply the short leg by 2

• Divide the short leg by 2

• Add the short leg to the longer leg

What is the formula to calculate the perimeter of a triangle?

• Sum of all side lengths

• Product of all side lengths

• Twice the sum of the legs

• Difference between the longest and shortest side

Why is it necessary to rationalize the denominator when calculating the perimeter?

• To simplify the expression

• To make the calculation more complex

• To ensure the denominator is a whole number

• To change the value of the expression

What is the final expression for the perimeter of the 30-60-90 triangle in the problem discussed?

• 12 sqrt 3 + 12

• 24 + 12 sqrt 3

• 12 + 12 sqrt 3

• 36 + 12 sqrt 3