Question

A triangle has two sides that measure 5 cm and 7 cm. Which of the following CANNOT be the measure of the third side?
A 3 cm
B 10 cm
C 17 cm

Answer 1

Answer:

Option C. $17\ cm$

Step-by-step 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.

so

Let

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

case 1)

$5+c> 7$

$c>7-5$

$c>2\ cm$

case 2)

$5+7> c$

$12> c$ ------> rewrite

$c<12\ cm$

The solution of the third side is the interval-------> $(2,12)$

therefore

$17\ cm$ can not be a measure of the third side