Answered

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

Verified Answer :

calculista

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