Two corners of an isosceles triangle are at #(4 ,2 )# and #(1 ,3 )#. If the triangle's area is #2 #, what are the lengths of the triangle's sides?
1 Answer
Sides:
or
Explanation:
There are two cases that need to be considered (see below).
For both cases I will refer to the line segment between the given point coordinates as
The length of
If
and given that the area is 2 (sq.units)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Case A:
Notice that the altitude
If the equal sides of the triangle are denoted as
then
(using the previously determined values for
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Case B:
Note that the altitude,
Since
and
(see prologue)
and