The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal, is

Question

KollegeApply · Accepted Answer

We are given that diameter and side of an equilateral triangle are equal. Let d and a are the diameter and side of circle and equilateral triangle respectively. $\therefore$ d=a We know that area of the circle =pir^2 Area of the equilateral triangle =sqrt3/4 a^2 Now we will find the ratio of the areas of circle and equilateral triangle. `$\therefore$ "Area of circle"/"Area of equilateral triangle"=(pir^2)/(sqrt3/4 a)` We know that radius is half of the diameter of the circle. `$\therefore$ "Area of circle"/"Area of equilateral triangle"=(pi (d/2)^2)/(sqrt3/4 a^2) $\therefore$ "Area of circle"/"Area of equilateral triangle"=(pixxd^$\frac{2}{4}$)/(sqrt3/4 a^2) Now we will substitute d=a in the above equation, $\therefore$ "Area of circle"/"Area of equilateral triangle"= ( pixxa^$\frac{2}{4}$)/(sqrt3/4 a^2) $\therefore$ "Area of circle"/"Area of equilateral triangle"=pi/sqrt3` Therefore, ratio of the areas of circle and equilateral triangle is pi:sqrt3

AChoose Your Answer