Question

If sides of a triangle have lengths 8 ft and 12 ft.

Answer 1

Answer:

$20 > c > 4$

Step-by-step explanation:

Given

$Sides =8\ and\ 12$

Required

The third side

To do this, we make use of the triangle inequality theorem which implies that:

$a + b > c$

$a + c > b$

$b + c > a$

Where

$a,b,c\to sides$

So, we have:

$8 + 12 > c$

$8 + c > 12$

$12 + c > 8$

Solve all inequalities

$8 + 12 > c$

$20 > c$

$8 + c > 12$

$c > 4$

$12 + c > 8$

$c > -4$

Ignore negative inequalities.

So, we have:

$20 > c$ and $c > 4$

Combine

$20 > c > 4$

The above implies that the third length is between 5 and 19 (inclusive)