Question

Two sides of a triangle are 5 and 15. Which of the following cannot be the third side? A. 6B. 12C. 19D. 20

Answer 1

Given:

Two sides of a triangle are 5 and 15.

To find:

Chose the correct option which cannot be the third side.

Step-by-step explanation:

The length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

Here, a sum of the two given sides is:

`5+15=20`

Also, the difference of two given sides,

`15-5=10`

So, the third side must be in between,

`\begin{gathered} 15-5<\text{ third side < 15 +}5 \\ 10<\text{ third side < 20} \end{gathered}`

Therefore, option (A) is not true according to the above property as 6 is less than 10.

Final answer:

Hence, (A) 6 cannot be the third side.