Question

homework: equations of proportional relationships
there is a proportional relationship between the side length of the equilateral triangle in feet, x, and the perimeter of the equilateral triangle is feet, y.
write an equation (in the form y = kx) for the relationship between x and y. simplify any fractions.

x (side length in feet) y (perimeter in feet)
1 3
2 6
4 12
5 15

Explanation:

Step1: Recall the formula for the perimeter of an equilateral triangle

The perimeter \( y \) of an equilateral triangle with side length \( x \) is \( y=x + x+x=3x \).

Step2: Check the proportionality constant using the table

For \( x = 1 \), \( y=3\times1 = 3 \); for \( x = 2 \), \( y=3\times2=6 \); for \( x = 4 \), \( y=3\times4 = 12 \); for \( x = 5 \), \( y=3\times5=15 \). The ratio \(\frac{y}{x}=\frac{3}{1}=\frac{6}{2}=\frac{12}{4}=\frac{15}{5}=3\).

Answer:

\(y = 3x\)