Choose the correct statements about triangles from the ones given below:
A. A triangle can be formed with sides 9 cm, 13 cm, 3 cm.
B. In ∆PQR, if ∠P =50°, ∠Q = 30°, then QR is the longest side of the triangle.
C. Area of an equilateral triangle of side 6 cm is 18√3 cm2.
D. In ∆DEF and ∆PQR, ∠
D = ∠P, ∠E = ∠Q and DF = PR. Then ∆DEF is congruent to
∆PQR.

The correct option is Only D.

Let us analyze each statement step-by-step to check its correctness:

Statement A: A triangle can be formed with sides 9 cm, 13 cm, 3 cm.
According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be strictly greater than the third side.
Let the side lengths be a = 9 cm, b = 13 cm, and c = 3 cm.
Checking the sum of the two shorter sides:
$9+3=12$
Since 12 is less than 13, the inequality a + c > b fails (12 < 13).
Thus, a triangle cannot be formed with these side lengths. Statement A is incorrect.

Statement B: In ∆PQR, if ∠P = 50°, ∠Q = 30°, then QR is the longest side of the triangle.
First, find the measure of the third angle, ∠R, using the angle sum property of a triangle:
$\angle P+\angle Q+\angle R=180°$
$50°+30°+\angle R=180°$
$\angle R=180°-80°=100°$
In any triangle, the side opposite to the largest angle is the longest side.
The largest angle is ∠R = 100°. The side opposite to ∠R is PQ.
Therefore, PQ is the longest side of ∆PQR, not QR.
Hence, Statement B is incorrect.

Statement C: Area of an equilateral triangle of side 6 cm is 18√3 cm².
The formula for the area of an equilateral triangle of side length a is:
$\text{Area}=\frac{\sqrt{3}}{4}{a}^2$
Substituting a = 6 cm:
$\text{Area}=\frac{\sqrt{3}}{4}\times 6^2=\frac{\sqrt{3}}{4}\times 36=9\sqrt{3}{\text{cm}}^2$
The area is 9√3 cm², not 18√3 cm².
Hence, Statement C is incorrect.

Statement D: In ∆DEF and ∆PQR, ∠D = ∠P, ∠E = ∠Q and DF = PR. Then ∆DEF is congruent to ∆PQR.
In ∆DEF and ∆PQR:
1. ∠D = ∠P (Given Angle)
2. ∠E = ∠Q (Given Angle)
Since two pairs of angles are equal, the third pair of angles must also be equal: ∠F = ∠R.
3. DF = PR (Given Side opposite to ∠E and ∠Q respectively)
By the Angle-Angle-Side (AAS) or Angle-Side-Angle (ASA) Congruence Criterion, ∆DEF ≅ ∆PQR.
Hence, Statement D is correct.

Conclusion: Only Statement D is correct.