Question

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.

Answer 1

Perimeter `=36.33` cm.

Explanation:

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

`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`