Question

How many diagonals does a triangle have?
$$\begin{gathered} (a)\text{ 0} \\ (b)\text{ 1} \\ (c)\text{ 2} \\ (d)\text{ 3} \end{gathered}$$

Answer 1

Hint: In this question we are being told to find the number of diagonals of a triangle. Now the number of diagonals of any n sided polygon can be found out using the direct formula $d={\displaystyle \frac{n\left(n-3\right)}{2}}$ where d is the number of diagonals and n is the number of sides of the polygon.

Complete step-by-step answer:

The general formula for number of diagonals (d) in any figure are
(n-3) multiply by the number of vertices and divide by 2.
$\Rightarrow d={\displaystyle \frac{n\left(n-3\right)}{2}}$ (Where n is the number of vertices)

As we know in a triangle there are three sides (see figure)
$\Rightarrow n=3$

Therefore number of diagonals in a triangle are
$\Rightarrow d={\displaystyle \frac{n\left(n-3\right)}{2}}={\displaystyle \frac{3\left(3-3\right)}{2}}={\displaystyle \frac{0}{2}}=0$

So the number of diagonals in a triangle are 0.
Hence option (A) is correct.

Note: Whenever we face such types of problems the key concept is simply to have the understanding of the direct formula to find the total number of diagonals. Such types of questions are generally direct formula based thus it is always advised to have a good gist of them. This will help to get on the right track and save a lot of time.