Question

A triangle has two sides length 10 to 14 wht value could the length of the third side be

Answer 1

Answer:

$4 < c < 24$

Step-by-step explanation:

Given

$a = 10$

$b = 14$

Required

The possible length of c

Using triangle inequality theorem, we have:

$a + b > c$

$a + c > b$

$b + c > a$

So, we have:

$a + b > c$

$10 + 14 > c$

$24 > c$

Also:

$a + c > b$

$14 + c > 10$

$c > 10 - 14$

$c > - 4$

Lastly;

$b + c > a$

$10 + c > 14$

$c > 14 - 10$

$c > 4$

Write out all inequalities without negative consideration

$24 > c$

$c > 4$

Rewrite as:

$c < 24$       $4 < c$

Writing both together, we have:

$4 < c < 24$

Hence, the third side can take its value from the range: $4 < c < 24$