Question

Trinny drew some equilateral triangles and measured their side lengths and perimeters. She decided that the perimeter of an equilateral triangle varies directly with its side length. Write an equation for the relationship and identify the constant of proportionality.

Answer 1

From the information given,

perimeter varies directly with side length

If two variables, a and b vary directly, then,

a = kb

where

k is the constant of proportionality

Given that

p varies directly with s, then

p = ks

We would solve for k

k = p/s

when p = 6, s = 2

k = 6/2 = 3

Thus, the constant of proportionality is 3

The equation for the relationship is

p = 3s