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 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