Statement 1: Area of given triangle ABC = 6 x 5 cm².

Statement 2: Area of given triangle ABC = $\dfrac{1}{2}$ x 6 x 4 cm².

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Draw a perpendicular bisector, AD.

The perpendicular bisector of the base also passes through the midpoint of the base, effectively dividing it into two equal segments.

BD = DC = $\dfrac{6}{2}$ = 3 cm

According to Pythagoras theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

⇒ Hypotenuse² = Base² + Height²

In Δ ABD,

⇒ AB² = AD² + BD²

⇒ 5² = AD² + 3²

⇒ 25 = AD² + 9

⇒ AD² = 25 - 9

⇒ AD² = 16

⇒ AD = $\sqrt{16}$

⇒ AD = 4 cm.

Using formula, area of triangle = $\dfrac{1}{2}$ x base x height

Here, base, BC = 6 cm and height, AD = 4 cm

⇒ Area of triangle = $\dfrac{1}{2}$ x 6 x 4 cm²

∴ Statement 1 is false, and statement 2 is true.

Hence, option 4 is the correct option.