Two sides of a triangle mesure 20cm and 30cm. What is the measure of the third side

Question

asked Jan 12, 2020 14.2k views

1 Answer

Carl · Answer 1 · 2020-01-19T00:45:17+0000

Answer:

All real numbers greater than
$10\ cm$ and less than
$50\ cm$

Explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

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

Applying the theorem

case A)

$20+30> c\\50> c\\ c< 50\ cm$

case B)

$20+c > 30\\c > 30-20\\c> 10\ cm$

The solution for the measure of the third side of the triangle is the interval

(10,50)

All real numbers greater than
$10\ cm$ and less than
$50\ cm$