The side opposite to the greatest angle in a triangle is the longest.
Here the biggest angle is the right angle, hence QR is the longest side of the triangle.

 

In a group of 3 numbers, if the square of the largest number is equal to the sum of the squares of the other two numbers, then, they form a Pythagorean triplet. So, the given statement is false.

Using angle sum property of a triangle,

$\angle$C = ${53}^{\circ }$ 
Since the sides are integers, and the triangle is right angled; the sides are 3 and 4 centimetres respectively.

Thus, magnitude of (AB +BC +∠C) = 3 + 4 + 53 = 60

By Exterior Angle property,
$\mathrm{âˆ}$ACD = $\mathrm{âˆ}$A + $\mathrm{âˆ}$B
$∴\text{Â}\mathrm{âˆ}$A =  $\mathrm{âˆ}$ACD - $\mathrm{âˆ}$B
            = ${120}^{∘}$​ -  ${50}^{∘}$​
            = ${70}^{∘}$​

Sides of lengths 5cm, 12cm and 13cm form sides of a right angled triangle.

The third side of a triangle must be greater than the difference between the other two sides.

That is, third side $>$ (16 - 13) which is 3.

Also, Sum of lengths of any two sides of a triangle is always greater than the third side.

That is, third side $<$ (16+13) which is 29.

Hence, a + b = 3 + 29 = 32.

Equilateral Triangle; Only in an equilateral triangle, all the altitudes and median are same lines. So, point A will be same as point N.

Calculation of angle: 1 Mark
Type of triangle: 1 Mark
In scalene triangles, all the angles are different. For $\angle ABC$ to be maximum, the other two angles must be minimum, but different (since scalene triangle).
The minimum value of the other angles will, therefore, be $1^{\circ }$ and $2^{\circ }$ as the angles have an integral value. Hence, for a scalene triangle the maximum integral value of $\angle ABC={177}^{\circ }$ [Angle sum property of a triangle].
The following triangle will be an Obtuse angled triangle , because one of the angle is greater than $90°$

Name and Explanation: 2 Marks
Yes, there exists a unique triangle for a particular set of sides. This is because 2 triangles having the same set of sides will be exactly identical. You can realize this by drawing 2 triangles with the same set of sides and then trying to superimpose one over the other. You will find that they are exactly identical.
If the two triangles have equal sides, then the two triangles are said to be congruent as equal sides are one of the criteria for congruency of triangles.