Question

If a $△PQR$ is constructed taking $QR=5\text{cm},$ $PQ=3\text{cm},$ and $PR=4\text{cm}$ then the correct order of the angles of the triangle is:

• A. $\angle P<\angle Q<\angle R$
• B. $\angle P>\angle Q<\angle R$
• C. $\angle P>\angle Q>\angle R$
• D. $\angle P<\angle Q>\angle R$

Answer 1

Answer: (C)

$\angle P>\angle Q>\angle R$

In a triangle, the angle is determined by its sides if it is given. The largest side will have the largest angle opposite to it. The smallest side will have the smallest angle opposite to it.

So, $QR=5\text{cm},$ is the largest side. Hence the angle opposite to it will also be largest that is$\angle P.$

Then the side$PR=4\text{cm},$, smaller than $QR$. Hence the $\angle Q$ will be smaller than $\angle P$

Finally, the smallest side is $PQ=3\text{cm}$ with its corresponding angle $\angle R$ is smallest.

Hence the option $C$ is correct.