Example 7.1.
Aunty Malanai is building a scale model of the waʻa Kānehūnāmoku. The original dimensions of the Kānehūnāmoku are:
- Mast: 25 ft
- Spar: 29 ft
- Boom: 19 ft
- Length: 29 ft
- Width: 11 ft
Aunty Malanai wants to make sure the mast on her scale model is \(10\) ft long. To maintain the proportions, what should be the lengths of the other dimensions on her scale model?
Solution 1.
Let’s denote the lengths of the dimensions on Aunty Malanai’s scale model as:
| Mast (Model): | \(m\) ft |
| Spar (Model): | \(s\) ft |
| Boom (Model): | \(b\) ft |
| Length (Model): | \(l\) ft |
| Width (Model): | \(w\) ft |
We know that the original mast length is \(25\) ft, and the new mast length for the scale model should be \(10\) ft. This gives us a ratio:
\begin{equation*}
\frac{{\text{Mast (Model)}}}{{\text{Mast}}} = \frac{m}{25} = \frac{10}{25}
\end{equation*}
Solving for \(m\text{,}\) we get:
\begin{equation*}
m = \frac{10}{25} \times 25 = 10 \text{ ft}
\end{equation*}
So, on Aunty Malanai’s scale model, the mast should be \(10\) ft long.
To maintain proportions, we can set up ratios for the other dimensions as well:
\begin{equation*}
\frac{{\text{Spar (Model)}}}{{\text{Spar}}} = \frac{s}{29}
\end{equation*}
\begin{equation*}
\frac{{\text{Boom (Model)}}}{{\text{Boom}}} = \frac{b}{19}
\end{equation*}
\begin{equation*}
\frac{{\text{Length (Model)}}}{{\text{Length}}} = \frac{l}{29}
\end{equation*}
\begin{equation*}
\frac{{\text{Width (Model)}}}{{\text{Width}}} = \frac{w}{11}
\end{equation*}
Since we’ve already found that the Mast (Model) is \(10\) ft, we can use this information to calculate the other dimensions on Aunty Malanai’s scale model.
Solution 2.
Scaling factor
Solution 3.
10 is 40 percent of 25. Multiply all by 40 percent
