How do you find the perimeter of a triangle if the altitude of an equilateral triangle is 32cm?

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Answer 1 · 2016-04-09T14:16:14

#64sqrt3# cm..

Ia a is a side length, altitude = #a ( cos 30^o )=asqrt3/2# = 32 cm.
#a = 64/sqrt3#cm.
So, the perimeter = 3a = #64sqrt3#cm.

Answer 2 · 2016-04-09T14:31:14

#color(red)("Solving without using Trig")#

#"perimeter "=64sqrt(3)color(white)(.) cm" "# (exact value)

#"perimeter "~~110.85color(white)(.) cm# to 2 decimal places

This is solvable by comparing to a standardised triangle and then using ratios.

Tony B

The perimeter of the standardised equilateral triangle is #3xx2=6" units"#

The 'altitude' of the standardised triangle is #sqrt(3)#

The given 'altitude' in the question is 32 cm

Let the length of 1 side be #L#
Let the perimeter be #P#

Then by ratio of #("triangle in question")/("standardised triangle")#

#=>L/2=32/sqrt(3)#

#=>L=(2xx32)/sqrt(3) = 64/sqrt(3)#

Then #P=3xx64/sqrt(3)#

#P=192/sqrt(3)#

Multiply by 1 but in the form of #1=sqrt(3)/sqrt(3)#

#P=(192sqrt(3))/3 = 64sqrt(3)#

As an approximate figure #P~~110.85# to 2 decimal places