Question

If the area of an equilateral triangle is 9v3 cm², find its perimeter.​

Answer 1

Answer:

Sides of equilateral Triangle is equal

Let side = x

Area of triangle = 1/2 x B x H

Height (h):

By Pythagoras theorem :

(Hyp)²=Opp² + adj²

x² = h² + (1/2)x

h² = x² - (1/2)x

h = √[x²-(x/2)]

Substituting h and B in area

9√3 = 1/2 * √[x²-(x/2)]

Squaring both side

81*3 = 1/4 * x²-(x/2)

243 = [x²-(x/2)]/4

x²-(x/2) = 243*4

x²-(x/2) = 972

(2x² - x)/2 = 972

2x² - x = 972 * 2

2x² - x = 1944

2x² -x - 1944 = 0

x ≈ 31.428

Perimeter = 3 (31.428)

=>94.484