Question

The ratio of the perimeter of an equilateral triangle having an altitude equal to the radius of a circle to the perimeter of an equilateral triangle inscribed in that circle is​

Answer 1

Answer:

assume dat the side of first triangle is a

the perimeter is 3a

so the altitude is (sqrt(3)*a)/2

it is the radius of the circle

now we know radius of circumcircle of an equilateral triangle of a side =bsqrt(3)

now

b/sqrt(3)=(sqrt(3)*a)/2

or 2b=3a

b=3a/2

perimeter is 3*(3a/2)

so ratio is 3a:(9a/2)

finally 2:37 years agoHelpfull: Yes(41) No(3)

sorry correct answr = 2:3

solution:in first equilateral triangle altitude =r(radius of a circle)so side will be (a)=2/sqrt(3)(u can find the side with help of pithagoras thrm in that triangle).so perimeter(P1) =3*a

now we have to find the perimeter of that equilateral triangle which is inside the circle of radius r.first find the side of this triangle that will be b=sqrt(3)(use cosine rule to find this side)so perimeter(P2)=3*b

now the ratio=P1/P2=3*a/3*b=2:3