Question

Find the length of the third side of the triangle inequality, if sides of a triangle have $a=4$ and $b=8$.

• A. $c=10$
• B. $c=2$
• C. $c=3$
• D. $c=4$

Answer 1

Answer: (A)

$c=10$

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.
Take option A: $a=4,b=8,c=10$
$4+8>10(a+b>c)$
$8+10>4(b+c>a)$
$4+10<8(a+c>b)$
Therefore, the third side, $c=10$ will satisfy the triangle inequality
Similarly check for option 2: $c=2$
$4+8>2(a+b>c)$
$8+2>10(b+c=a)$
$4+2<8(a+c<b)$
Hence, the second option will not satisfying the triangle inequality.
Similarly check for option $3$ and $4$.
Here, the third side of the triangle inequality, $c=10$.