Triangle Height and Area Concepts

The video tutorial explains how to determine the base and height of a triangle given its area and a relationship between the base and height. It introduces variables for the height and base, applies the area formula for a triangle, and sets up a quadratic equation. The equation is solved to find the height, and the base is calculated using the height. The tutorial emphasizes the importance of positive values for geometric dimensions.

What is the relationship between the base and height of the triangle?

• The base is twice the height.

• The base is six inches more than three times the height.

• The base is equal to the height.

• The base is half the height.

What is the formula used to calculate the area of a triangle?

• Area = base + height

• Area = base * height

• Area = base / height

• Area = 1/2 * base * height

What is the first step in solving the quadratic equation for the height?

• Clear the parentheses by distributing.

• Divide both sides by 2.

• Multiply both sides by 3.

• Add 120 to both sides.

What is the greatest common factor used to simplify the quadratic equation?

• 5

• 2

• 3

• 10

What are the possible solutions for the height of the triangle?

• h = 6 and h = -6

• h = 10 and h = -8

• h = 12 and h = -12

• h = 8 and h = -10

Why is the solution h = -10 excluded?

• Because it is not a whole number.

• Because it is not a positive number.

• Because it is not a rational number.

• Because it is not an integer.

What is the final height of the triangle?

• 12 inches

• 8 inches

• 6 inches

• 10 inches

What expression represents the base of the triangle?

• 3h + 6

• 2h + 6

• h + 6

• h - 6

What is the length of the base when the height is 8 inches?

• 24 inches

• 32 inches

• 28 inches

• 30 inches

What is the area of the triangle?

• 100 square inches

• 120 square inches

• 140 square inches

• 160 square inches