Question

In $∆PQR$,

• A. $PQ–QR>PR$
• B. $PQ+QR<PR$
• C. $PQ–QR<PR$
• D. $PQ+PR<QR$

Answer 1

The correct option is C

$PQ–QR<PR$

Explanation for the correct option:

In a triangle, the sum of the lengths of two sides of a triangle should always be greater than the third side.

In $∆PQR$

$$\begin{gathered} PR+QR>PQ \\ \Rightarrow PR>PQ-QR \end{gathered}$$

$\Rightarrow PQ–QR<PR$, the sum of two sides is greater than the third.

Explanation for the incorrect options:

1. In $PQ–QR>PR$, the sum of two sides is not greater than the third.
2. In $PQ+QR<PR$, the sum of two sides is not greater than the third.
3. In $PQ+PR<QR$, the sum of two sides is not greater than the third.

Hence, option $\left(\mathrm{C}\right)$ is correct.