Triangle Area and Perimeter Concepts

The video tutorial explains how to find the perimeter of an equilateral triangle with a given area of 177 square centimeters. It uses the Pythagorean theorem and the area formula for a triangle, avoiding trigonometry. The tutorial sets the side length as 2X, derives the height in terms of X, and solves for X using the area equation. Finally, it calculates the perimeter as 6X, resulting in approximately 60.66 centimeters.

What is the area of the equilateral triangle given in the problem?

• 150 square centimeters

• 177 square centimeters

• 100 square centimeters

• 200 square centimeters

Which theorem is used to find the height of the triangle?

• Sine Rule

• Cosine Rule

• Pythagorean Theorem

• Law of Tangents

If the side of the triangle is 2x, what is the length of the segment bisected by the height?

• 4x

• x

• 2x

• 3x

What is the expression for the height of the triangle in terms of x?

• x√2

• x√3

• x

• 2x

Why is only the positive square root considered when solving for the height?

• Because it is easier to calculate

• Because height cannot be negative

• Because it is a convention

• Because it simplifies the equation

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

• base + height

• 1/3 x base x height

• base x height

• 1/2 x base x height

What is the simplified equation to solve for x after using the area formula?

• x = 177

• x^2 = 177√3

• x^2√3 = 177

• x^2 = 177

What is the approximate value of x derived from the equation?

• 10.11

• 11.11

• 9.11

• 12.11

How is the perimeter of the triangle calculated?

• 3x

• 4x

• 5x

• 6x

What is the final calculated perimeter of the triangle?

• 50.66 cm

• 60.66 cm

• 70.66 cm

• 80.66 cm