The area of a circle inscribed in an equilateral triangle is 154 square centimeters. What is the perimeter of the triangle? Use pi=22/7 and square root of 3= 1.73.

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Alan P. Share
Jan 6, 2016

Answer:

Perimeter #=36.33# cm.

Explanation:

This is Geometry, so lets look at at a picture of what we are dealing with:
enter image source here

#A_("circle") = pi*r^2color(white)("XXX")rarrcolor(white)("XXX")r=sqrt(A/pi)#

We are told
#color(white)("XXX")A=152 "cm"^2#
and to use
#color(white)("XXX")pi = 22/7#

#rArr r= 7# (after some minor arithmetic)

If #s# is the length of one side of the equilateral triangle and #t# is half of #s#

#color(white)("XXX")t=r*cos(60^@)#

#color(white)("XXXx")=7*sqrt(3)/2#

and
#color(white)("XXX")s=2t = 7*sqrt(3)#

#color(white)("XXXx")=12.11# (since we are told to use #sqrt(3)=1.73#)

Perimeter #=3s#

#color(white)("XXXXXX")=3 xx 12.11 = 36.33#

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