How can I figure out what the scale of an object is going to be?

Question

I've been stuck on this question for weeks can anyone please explain this to me? Cate drew an animal that she wants to create. She said that it would obviously be bigger than the drawing because she used a scale of $1cm:13 inches$. Based upon Cate's drawing how tall would this animal be in real life? The drawing is $7.2 cm$ tall so I came up with $7 ft. 8 in$. tall which the teacher said was correct. The next question that I'm stuck on is Libby suggested they try to make the new animal exactly $5 ft$ tall. What scale should they use to go with her idea? How do you figure out the scale of an object?

Answer 1

Firstly the first convertion should be \begin{eqnarray*} 7.2 cm \rightarrow 93.6 = \underbrace{84}_{7 \times 12}+9.6 = 7 ft 9.6 inches \end{eqnarray*} To convert $5 ft$ back, convert to inches \begin{eqnarray*} x cm \rightarrow 5 ft = 60 inches \end{eqnarray*} and divide by $13$ ($60/13 =4.615 \cdots$) \begin{eqnarray*} \color{red}{4.6 cm} \rightarrow 5 ft = 60 inches \end{eqnarray*}

Edit: The scale factor required for Libby's animal will be $60/7.2= 8 \frac{1}{3}$ inches per cm \begin{eqnarray*} 7.2 cm \underbrace{\rightarrow}_{\color{blue}{ \times 8 \frac{1}{3}}} 5 ft = 60 inches \end{eqnarray*}