The altitude of an equilateral triangle is 4.2 meters long. Find the perimeter of the triangle.

Step-by-step explanation:

s = √( 4.2*4.2 + (s/2)(s/2) )

s = √( 4.2*4.2 + (s^2/4) )

s^2= 4.2*4.2 + (s^2/4)

s^2 - (s^2/4) = 4.2*4.2

(4s^2/4) - (s^2/4) = 4.2*4.2

(3s^2/4) = 4.2*4.2

(3/4)s^2 = 4.2*4.2

s^2= 4.2*4.2*(4/3)

s = √( 4.2*4.2*(4/3) )

s = 2*4.2 * √( 1/3 )

s = 4.84974226119

perimeter = 3 * 4.84974226119

perimeter = 14.5492267836 meters

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

step-by-step explanation: