Question

Sardis was drawing a triangle. The first segment he drew was 10 centimeters. The 2nd side he drew was 12 centimeters. How long would the 3rd side have to be to create a triangle? Watch the video for support.

Answer 1

see the explanation

Explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the triangle inequality theorem

Let

c ----> the measure of the length of the third side

1)
`10+12 > c`

`22 > c\\c < 22 cm`

2)
`c+10>12`

`c > 12-10\\c >2 cm`

so

The solution for the length of the third side is the interval (2,22)

All real numbers greater than 2 centimeters and less than 22 centimeters