Question

A prallelogram has a height of 4 cm and a base of 8 cm. After being dilated, the resulting image has an area of 8 cm2. What scale factor was applied to the base and height of the original parallelogram?​

Answer 1

Answer:

The scale factor applied was 1/2

Step-by-step explanation:

step 1

Find the area of the original parallelogram

A=bh

substtute the given values

$A=(8)(4)=32\ cm^2$

step 2

Find the scale factor

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> scale factor

x ---> area of the dilated parallelogram

y ---> area of the original paeallelogram

so

$z^2=\frac{x}{y}$

we have

$x=8\ cm^2\\y=32\ cm^2$

substitute

$z^2=\frac{8}{32}$

simplify

$z^2=\frac{1}{4}$

therefore

$z=\frac{1}{2}$

The scale factor applied was 1/2