UPSC CAPF Assistant Commandant Model Paper 7

GIVEN:
Area of an equilateral triangle = 25√3 cm2
CONCEPT:
Mensuration
FORMULA USED:
Area of triangle =

1

2

× Base × height
CALCULATION:
Let the side of the equilateral triangle = ‘d’ cm
So, the height of the equilateral triangle = (d√3/2) cm
From the question:
(1/2) × d × (d√3/2) = 25√3
⇒ d2=100
⇒ d = 10 cm
Height of the equilateral triangle = side of the square = 10 × √3/2 = 5√3 cm
So,
Area of the square = 5√3 × 5√3 = 75 cm2