what is the area of the given right angle triangle ?
I. Length of the hypotenuse is 5 cm
II.perimeter of the triangle is four times its base
III. one of the angles of the triangle is 60 degrees

To find the area of right angled triangle, we need to know the base and height or the length of any side if its a 30-60-90 triangle

From statement I and III, two angles are 90° and 60°, => Third angle = 30°

In a 30-60-90 triangle, the hypotenuse is always twice as long as the side opposite the 30° angle and the side opposite the 60° angle is √3 times as long as the side opposite the 30° angle.

The ratio of sides opposite 30°, 60° and 90° angles =1 : $$\sqrt{3}$$ : 2

Length of the side opposite the 90° angle (hypotenuse) = 5 cm

=> Length of side opposite the 30° angle = $$\frac{5}{2}=2.5$$ cm

and length of side opposite to 60° angle = $$2.5 \sqrt{3}$$ cm

$$\therefore$$ Area of triangle = $$\frac{1}{2} \times 2.5 \times 2.5 \sqrt{3} = 3.125\sqrt{3}$$ $$cm^2$$

Thus, statement II is redundant.

=> Ans - (B)