Question

an equilateral triangle circumscribed all the circles each with radius 10 cm. what is the perimeter of the equilateral triangle

Answer 1

Answer:

An equilateral triangle circumscribed all the circles each with radius 10 cm. The perimeter of the equilateral triangle = 30√3 cm (51.96 cm)

Step-by-step explanation:

An equilateral triangle circumscribed inside the circle

Let say side of equilateral triangle = a cm

area of equilateral triangle = √3 a²/4 cm²

if we connect all the vertices of triangle from center it will divide triangle into three equal triangles

so area of one such triangle = (1/3) (√3 a²/4) = √3 a²/12 cm²

Area of one such triangle = (1/2) a * h

h = √(r² - (a/2)²)  r = radius

√3 a²/12 = (1/2) a * √(r² - (a/2)²)

=> √3 a/6 = √(10² - (a/2)²)

Squaring both sides

3a²/36 = 100 - a²/4

=> a²/12 = 100 - a²/4

=> a² = 1200 - 3a²

=> 4a² = 1200

=> a² = 300

=> a = 10√3

Side of equilateral triangle = 10√3 cm

Perimeter = 3a = 30√3 cm = 51.96 cm

Answer 2

Answer:

60(2+✓3)

Step-by-step explanation:

this may will help you