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 the side - length of the equilateral triangle

An equilateral triangle has three equal sides. Let the side - length be $a$. The perimeter $P = 3a$. Given $P = 624$ cm, then $3a=624$, so $a=\frac{624}{3}=208$ cm.

Step2: Relate the side - length and height of an equilateral triangle

The height $h$ of an equilateral triangle with side - length $a$ is given by the formula $h = \frac{\sqrt{3}}{2}a$. We know $h = k\sqrt{3}$ and $a = 208$ cm. Substituting $a$ into the height formula, we get $h=\frac{\sqrt{3}}{2}\times208 = 104\sqrt{3}$ cm. Since $h = k\sqrt{3}$, then $k = 104$.

Answer:

104