Pythagorean Theorem Problem Solving

This video tutorial demonstrates solving a right triangle problem using the Pythagorean theorem. The instructor sets up the equation by squaring each side of the triangle, expands and simplifies the terms, and then solves the resulting quadratic equation. The solution is verified for validity, ensuring it satisfies the Pythagorean theorem.

What is the initial setup of the problem involving the Pythagorean theorem?

• A rectangle with sides 4x and 5x - 2

• A right triangle with sides 2x + 1, 4x, and 5x - 2

• A square with sides 2x, 4x, and 5x

• A circle with radius 2x + 1

What is the first step in solving the equation using the Pythagorean theorem?

• Subtracting the hypotenuse from the legs

• Dividing each side by x

• Squaring each side of the triangle

• Adding all sides together

What is the result of squaring the expression 2(x + 1)?

• x^2 + 2x + 1

• 4x^2 + 4x + 1

• 4(x^2 + 2x + 1)

• 2x^2 + 2x + 1

What is the expanded form of (5x - 2)^2?

• 25x^2 - 20x + 4

• 25x^2 + 20x + 4

• 5x^2 - 4x + 4

• 25x^2 - 4

What is the next step after expanding the expressions on both sides?

• Multiply all terms by 2

• Subtract the smaller expression from the larger one

• Divide by the greatest common factor

• Combine like terms

What is the result of 4x^2 + 8x + 4?

• 4x^2 + 8x + 4

• 20x^2 + 8x + 4

• 20x^2 + 4

• 16x^2 + 8x + 4

How do you recognize the equation as a quadratic equation?

• It has a term with x

• It has a term with x^3

• It has a term with x^2

• It has a constant term

What is the purpose of rearranging the equation to set one side to zero?

• To prepare for factoring

• To eliminate x

• To simplify the equation

• To find the hypotenuse

What is the result of subtracting 20x from both sides?

• 25x^2 + 28x

• 5x^2 - 28x

• 25x^2 - 28x

• 5x^2 + 28x

What is the result of subtracting 4 from both sides?

• 4

• 16

• 0

• 8