Question

Rectangle EFGH
is a scale drawing of rectangle ABCD.
Rectangle ABCD has a width of 4 & a length of 8. Rectangle EFGH has a width of 10 & a length of 20.

© 2018 StrongMind. Created using GeoGebra.

What is the scale factor?

Enter your answer as a fraction in simplest form, like this: 42/53

Answer 1

To find the scale factor between rectangle ABCD and rectangle EFGH, we compare the dimensions of the two rectangles.

The dimensions of rectangle ABCD are:
- Width: 4
- Length: 8

The dimensions of rectangle EFGH are:
- Width: 10
- Length: 20

To find the scale factor for the width:

\[
\text{Scale factor (width)} = \frac{\text{Width of EFGH}}{\text{Width of ABCD}} = \frac{10}{4} = \frac{5}{2}
\]

To find the scale factor for the length:

\[
\text{Scale factor (length)} = \frac{\text{Length of EFGH}}{\text{Length of ABCD}} = \frac{20}{8} = \frac{5}{2}
\]

Both the scale factors for width and length are the same, thus the overall scale factor from rectangle ABCD to rectangle EFGH is:

\[
\text{Scale factor} = \frac{5}{2}
\]

So the scale factor is \(\frac{5}{2}\).