Question

problems 5 - 7: here is some information about the side lengths of two scaled copies, triangle a and triangle b.

1. complete the table to determine the missing side lengths of each triangle.
2. what is a constant of proportionality in this relationship?

Explanation:

Step1: Find the constant of proportionality

We know that when the side - length of triangle A is 1 and of triangle B is 3, the constant of proportionality $k$ is found by $\frac{\text{Side length of B}}{\text{Side length of A}}$. So $k = 3\div1=3$.

Step2: Find the missing side - length for $\text{Side length of A}=\frac{1}{2}$

Using the formula $\text{Side length of B}=k\times\text{Side length of A}$, substitute $k = 3$ and $\text{Side length of A}=\frac{1}{2}$. Then $\text{Side length of B}=3\times\frac{1}{2}=\frac{3}{2}$.

Step3: Find the missing side - length for $\text{Side length of B}=8$

Using the formula $\text{Side length of A}=\frac{\text{Side length of B}}{k}$, substitute $k = 3$ and $\text{Side length of B}=8$. Then $\text{Side length of A}=\frac{8}{3}$.

Step4: Find the missing side - length for $\text{Side length of A}=\frac{4}{3}$

Using the formula $\text{Side length of B}=k\times\text{Side length of A}$, substitute $k = 3$ and $\text{Side length of A}=\frac{4}{3}$. Then $\text{Side length of B}=3\times\frac{4}{3}=4$.

5.

Side Length of Triangle A (in.)	Side Length of Triangle B (in.)
$\frac{1}{2}$	$\frac{3}{2}$
$\frac{8}{3}$	8
$\frac{4}{3}$	4

Answer:

for question 6:
The constant of proportionality is 3.