A circle is inscribed in an equilateral triangle of side √3a units. Which of the following is the area of the square constructed with a diameter of the circle as a side (in sq. units)?
Answers
Answer:
The required area of square is a sq. units
Step-by-step explanation:
Given, side of an equilateral triangle as √3a units.
We know that centroid, orthocentre and circumcentre of an equilateral triangle are equal.
Altitude of equilateral triangle = √3/2(side)
= √3/2(√3 a)
= 3a/2
According to a theorem, the orthocentre of equilateral triangle divides the altitude in ratio 2:1
so the line joining the center of circle with the base of equilateral triangle is 1/3 part of altitude that is the radius of the circle.
radius = 1/3 (3a/2)
= a/2
diameter of circle = 2(radius)
= 2(a/2)
= a units
side of square = diameter of circle = a
area of square = (side)²
= (a)²
= a sq. units
Hence, area of square is a sq. units.
Answer:
(edit) its (a) sq units my apologies
as the square was constructed with diameter as a side
here's the solution
happy to help!
