Question

Part A.. What is the scale factor (as a decimal) was used to create the larger rectangle?Part B. Using the scale factor you just foujd, what is the length be of the unknown side on the smaller rectangle?

Answer 1

From the given picture we can see

A small rectangle with a side of length 6 cm

The corresponding side of the large rectangle is 21 cm

To find the scale factor of enlargement we will divide 21 by 6

`\begin{gathered} S.F=(21)/(6) \\ S.F=3.5 \end{gathered}`

Part A:

The answer is 3.5

To find the missing side of the small rectangle we will use the scale factor with the corresponding side of the large rectangle which is 52.5 cm

`(52.5)/(x)=3.5`

By using the cross-multiplication

`\begin{gathered} x*3.5=52.5 \\ 3.5x=52.5 \end{gathered}`

Divide both sides by 3.5

`\begin{gathered} (3.5x)/(3.5)=(52.5)/(3.5) \\ x=15 \end{gathered}`

Part B:

The missing side in the small rectangle is 15 cm