Question

The polygons below are similar, but not necessarily drawn to scale. Find x.

4 +
36
AM

Answer 1

x = 20

Explanation:

In similar polygons, all corresponding sides are proportional. The scale factor between AB and DE is the same as between AC and DF.

`(DE)/(AB)=(DF)/(AC)\\\\(4+x)/(4)=(36)/(6)\\\\6(4+x)=4(36)\\24+6x=144\\6x=120\\x=20`

You can confirm that by plugging it back into the original equation:

`(4+x)/(4)=(36)/(6)\\\\(4+(20))/(4)=(36)/(6)\\\\(24)/(4)=(36)/(6)\\\\6=6`