Guina made a scale drawing of a window she is making for her house.

1 centimeter = 3 inches. Triangle A B C. Side A is 4 centimeters, side B is 3 centimeters, and side C is 5 centimeters.
Which proportion could Guina use to find the length of side B?
StartFraction 1 centimeters over 3 inches EndFraction = StartFraction 3 centimeters over x centimeters EndFraction
StartFraction 3 centimeters over 1 centimeter EndFraction = StartFraction x centimeters over 3 centimeters EndFraction
StartFraction 1 centimeter over 3 inches EndFraction = StartFraction 3 centimeters over x inches EndFraction
StartFraction 3 inches over 3 centimeters EndFraction = StartFraction x inches over 1 centimeter

1 answer

To find the length of side B in inches using the conversion factor provided (1 centimeter = 3 inches), Guina needs to set up a proportion that relates the centimeters to inches.

Since side B is 3 centimeters in the drawing, we want to convert that to inches. We can express this as follows:

  • The equivalent in inches can be found using the ratio \( \frac{1 \text{ cm}}{3 \text{ inches}} \).

To set up the proportion where 3 centimeters corresponds to \( x \) inches, the correct proportion would be:

\[ \frac{1 \text{ cm}}{3 \text{ inches}} = \frac{3 \text{ cm}}{x \text{ inches}} \]

This matches the third option in your list:

StartFraction 1 centimeters over 3 inches EndFraction = StartFraction 3 centimeters over x inches EndFraction.

This proportion can now be solved to find \( x \), which will give you the length of side B in inches.