Question

6.1 Scale Factoring Black Pearl 1 1 point What was the actual If the Black Pearl's model is 1:150 scale. The model measures 26.4 in in length and it has 22.6 in height. Type your answer... What was the real ship's size? 2 1 point What was the actual Type your answer.

Answer 1

To solve the exercise you can use proportions, like this:

*For the length

`\begin{gathered} (1)/(150)=\frac{26.4\text{ in}}{x} \\ \text{ Use Cross multiplication} \\ 1\cdot x=26.4\text{ in}\cdot150 \\ x=3960\text{ in} \end{gathered}`

*For the height

`\begin{gathered} (1)/(150)=\frac{22.6\text{ in}}{x} \\ \text{ Use Cross multiplication} \\ 1\cdot x=22.6\text{ in}\cdot150 \\ x=3390\text{ in} \end{gathered}`

Then, the actual size of the ship is 3960 inches in length and 3390 inches in height.

Now, to convert these measurements to feet, you can use the proportion:

*For the length

`\begin{gathered} \frac{1\text{ ft}}{12\text{ in}}=\frac{x\text{ ft}}{3960\text{ in}} \\ \text{ Multiply by 3960 in on both sides of the equation} \\ \frac{1\text{ ft}}{12\text{ in}}\cdot\text{3960 in}=\frac{x\text{ ft}}{3960\text{ in}}\cdot\text{3960 in} \\ \frac{1\text{ ft}\cdot3960\text{ in}}{12\text{ in}}=x \\ 330\text{ ft }=x \end{gathered}`

*For the height:

`\begin{gathered} \frac{1\text{ ft}}{12\text{ in}}=\frac{x\text{ ft}}{3390\text{ in}} \\ \text{ Multiply by 3390 in on both sides of the equation} \\ \frac{1\text{ ft}}{12\text{ in}}\cdot3390\text{ in}=\frac{x\text{ ft}}{3390\text{ in}}\cdot3390\text{ in} \\ \frac{1\text{ ft}\cdot3390\text{ in}}{12\text{ in}}=x \\ 282.5\text{ ft}=x \end{gathered}`

Therefore, the actual size of the ship is 330 feet in length and 282.5 feet in height.