SSC CHSL 2023 PYQ — Question 21

The correct answer is option 4. i.e. The area of an isosceles triangle with sides 2a, 2a and 3a is $\frac{3\sqrt3\,{a^2}}{2}$.

Option 1 : Given the largest side of a triangle = l

Other sides of triangle a,b < l

The height of the triangle h² = l² - b²

So, h < l and bh < l²

Now, the area of the triangle A = ½ bh 

Hence, A < l²/2 i.e. this statement is true

Option 2 : If the sides of a triangle are in the ration 13 ∶ 5 ∶ 12,

5,12,13 is a tripilate of a right angled triangle 

Hence, In a right angle triangle, one angle is 90º and other two angles are acute angle. 

Option 3 : The triangle EFG formed the joining mid points of the sides of a triangle ABC

Hence, the area of the triangle EFG = 1/4 × Area of the triangle ABC

Option 4 : An isosceles triangle with sides 2a, 2a and 3a

Area of isosceles triangle A = ½[√(a² − b² ⁄4) × b]

where a = 2a and b = 3a

A = (3a/2) [√(4a² − 9a² ⁄4)] = (3a/4) √7 a = 3√7 a²/4

Hence, this statement is wrong