Question

On an anual basketball court,the bench is 9 meters long, How long should the bench be on the scale drawing if 1 cm represents 2 meters

Answer 1

4.5 cm

Explanation

Step 1

find the scale factor

$\begin{gathered} \text{1 cm }\rightarrow\text{ 2 meters} \\ 100\text{ cm = 1 meter, then} \\ 1\text{ cm }\rightarrow200\text{ cms} \\ 1\colon200\text{ is the scale factor} \end{gathered}$

Step 2

use a rule of thee to find the length in the drawing

Let

x represents the length in the drawing

9 meters= 9*100cm= 900 cms

if

$\begin{gathered} 1\text{ cm at drawing}\rightarrow200\text{ cm at real bench} \\ 1\rightarrow200 \\ \text{then} \\ x\text{ cm }\rightarrow900 \end{gathered}$

the proportion is the same, so

$\begin{gathered} \frac{1}{200}=\frac{x}{900} \\ \end{gathered}$

Step 3

solve for x

$\begin{gathered} \frac{1}{200}=\frac{x}{900} \\ 900\cdot1=200\cdot x \\ x=\frac{900}{200} \\ x=4.5 \end{gathered}$

so, the answer is 4.5 cm