Question

the perimeter of an equilateral triangle is 624 centimeters. the height of this triangle is ( ksqrt{3} ) centimeters, where ( k ) is a constant. what is the value of ( k )?

Explanation:

Step1: Find side length of triangle

The perimeter of an equilateral triangle is $P = 3s$, so side length $s = \frac{624}{3} = 208$ cm.

Step2: Relate height to side length

For an equilateral triangle, height $h = \frac{s\sqrt{3}}{2}$. Substitute $s=208$:
$h = \frac{208\sqrt{3}}{2} = 104\sqrt{3}$

Step3: Match to given height form

Given $h = k\sqrt{3}$, so $k = 104$.

Answer:

104