Triangle Properties and Factorization

The video tutorial covers algebraic problem-solving, including factoring and solving equations. It introduces special right triangles, specifically 45-45-90 and 30-60-90 triangles, and demonstrates how to solve related problems. The tutorial also explores calculating perimeters and applying geometry concepts in various scenarios.

What is the value of y if 2y is equidistant from 58 and 21?

• y = 5

• y = 4

• y = 3

• y = 6

Which of the following is a correct factorization of 2x^2 + 3x - 9?

• (2x - 3)(x + 3)

• (x + 3)(2x - 3)

• (x - 3)(2x + 3)

• (2x + 3)(x - 3)

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

• 5√2

• 10

• 5

• 10√2

In a 30-60-90 triangle, if the shorter leg is 3, what is the length of the hypotenuse?

• 3√3

• 6√3

• 6

• 3

What is the perimeter of a square with a diagonal of 12 cm?

• 24√2 cm

• 48 cm

• 24 cm

• 12√2 cm

In an isosceles right triangle with legs of 3 cm, what is the length of the hypotenuse?

• 3√2 cm

• 3 cm

• 6 cm

• 6√2 cm

What is the perimeter of an isosceles trapezoid with bases of 10 cm and 24 cm, and legs of 7√2 cm?

• 34 + 14√2 cm

• 24 + 14√2 cm

• 48 + 14√2 cm

• 48 cm