Exploring Quadratic Equations in Right Triangles

What is the side opposite the right angle in a right triangle called?

• Base

• Altitude

• Leg

• Hypotenuse

Which sides of the right triangle are known as legs?

• The two shortest sides

• The two sides forming the right angle

• The two longest sides

• The side opposite the right angle and one adjacent side

How does the Pythagorean theorem relate to quadratic equations?

• By using linear equations

• By using squares of side lengths

• By using cube of side lengths

• By using square roots

What is the length of the hypotenuse in the problem discussed?

• 7 cm

• 5 cm

• 12 cm

• 13 cm

How much longer is the longer leg compared to the shorter leg in the example?

• 7 cm

• 5 cm

• 13 cm

• 12 cm

What form does the equation take after applying the Pythagorean theorem in the example?

• Linear equation

• Quadratic equation

• Cubic equation

• Trigonometric equation

What is the simplified form of the quadratic equation derived from the triangle's side lengths?

• 2x^2 + 13x - 120 = 0

• 2x^2 + 14x - 120 = 0

• x^2 + 7x + 13 = 0

• x^2 + 14x + 49 = 169

Which value of x is not possible for the length of the shorter leg?

• 12

• 7

• 5

• -12

What is the length of the longer leg when the shorter leg is 5 cm?

• 12 cm

• 17 cm

• 10 cm

• 7 cm

Does 5 squared plus 12 squared equal 13 squared?

• Insufficient information

• Irrelevant to the Pythagorean theorem

• Yes

• No