Question

Find the length of each side of an equilateral triangle of area
$\sqrt[4]{3} \: cm {}^{2}$
​

Answer 1

Step-by-step explanation:

it is not clear whether area = 4*√3 or 3^(1/4)

case 1: if area is 3^(1/4)

given

area of equilateral triangle = 3^(1/4) cm2

we know that area of equilateral triangle

= (√3/4) *(side)^2

thus,

(√3/4)*(side)^2 = 3^(1/4)

(side)^2 = 3^(1/4) * 4/√3

(side)^2 = 4/3^(1/2 - 1/4)

side^2 = 4/3^1/4

side = 2*3^(-1/8)

case 2: if area is equal to 4√3

(√3/4)*(side)^2 = 4*√3

side ^2 = 4*√3*4/√3

side^2 = 16

side = 4 (taking positive value only)