Question 626310
Find the length of a diagonal of a rhombus when the area is 48 and the other diagonal is 12.
<pre>
Let the rhombus be ABCD with diagonal AC given = 12, and we are
to find the length of diagonal BD:

{{{drawing(2000/7,400,-5,5,-7,7,
red(line(0,6,0,-6)), green(line(-4,0,4,0)),locate(.2,0,E),
line(-4,0,0,6), line(0,6,4,0), line(-4,0,0,-6), line(0,-6,4,0),
locate(-4.5,.3,B),locate(4.2,.3,D), locate(-.2,-6,C), locate(-.2,6.5,A)


 )}}}

The diagonals of a rhombus are perpendicular bisectors of each
other.  Therefore since AC is given equal to 12, AE = EC = 6.

Since triangle ABD and CBD are congruent, and the entire rhombus
has area 48, each of those triangles has area 24.

Area of triangle ABD = {{{1/2}}}base×height

                  24 = {{{1/2}}}BD·AE
                  24 = {{{1/2}}}BD·6
                  24 = 3·BD
                   8 = BD

Edwin</pre>