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

Option C.
`17\ cm`

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