UPSC CDS 1 2022 Math Paper

Given:
Area of each smaller equilateral triangle =9√3cm2
Concept Used:
Area of equilateral triangle =√3a2∕4
Height of equilateral triangle =√‌3a∕2
Where, a= side of the equilateral triangle
Calculation:Let the side length of each smaller triangle be a cm Since the area of each smaller equilateral triangle =9√3cm2
So, √3a2∕4=9√3
⇒a=6cm
So, the side of bigger equilateral triangle ABC=6×3=18cm
So, Height AD of the bigger equilateral triangle =(√3×18)∕2=9√3cm
∴ The required height of the bigger equilateral triangle is 9√3cm .