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Example Question #11 : Quadrilaterals
Figure NOT drawn to scale
Refer to the above figure.
True or false: Rectangle Rectangle
.
False
True
False
Two rectangles are similar if and only if their sides are in proportion. Specifically,
Rectangle Rectangle
if
Since is located at the point
, it follows that
and
. Since
is located at the point
, it follows that
and
. Substituting in the aforementioned proportion statement, we get
.
Reducing to lowest terms, this is
.
This is false, so Rectangle Rectangle
.
Example Question #11 : Rectangles
Consider the similar rectangles and
shown here. The lengths of the following sides are given:
What is the length of the side ?
Comparing the sides and
, we see that
is
the length of
, as shown here:
.
Since these two rectangles are similar, all pairs of corresponding sides are similar. Hence, the ratio of to
is also
, and we can calculate the length of
by setting up and solving a proportion:
.
Hence, the length of the side is
units.
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