Triangle Side Lengths and Angles

The video tutorial explores a triangle with sides 3, 4, and X. It begins by discussing the well-known 3-4-5 triangle, where X equals 5. The tutorial then examines scenarios where the angle between sides 3 and 4 is greater than 90 degrees, allowing X to be more than 5 but less than 7. Conversely, if the angle is less than 90 degrees, X can be as small as 2. The final conclusion is that X must be greater than 1 but less than 7, adhering to the triangle inequality theorem.

What are the given side lengths of the triangle in the problem?

• 4 and 5

• 3 and 4

• 5 and 6

• 6 and 7

What is the common third side length in a 3-4-5 triangle?

• 7

• 5

• 6

• 4

If the angle between sides 3 and 4 is greater than 90 degrees, what is the range for the third side?

• More than 5 but less than 7

• Between 3 and 5

• Less than 3

• More than 7

Why must the third side be less than the sum of the other two sides?

• To ensure the triangle is equilateral

• To ensure the triangle is isosceles

• To ensure the triangle is valid

• To ensure the triangle is right-angled

What is the minimum possible length for the third side if the angle is less than 90 degrees?

• 4

• 1

• 2

• 3

Why must the third side be greater than the difference of the other two sides?

• To ensure the triangle is right-angled

• To ensure the triangle is valid

• To ensure the triangle is isosceles

• To ensure the triangle is equilateral

What is the final range for the third side length?

• Greater than 3 but less than 9

• Greater than 0 but less than 6

• Greater than 1 but less than 7

• Greater than 2 but less than 8