SOLUTION: Find the length of a diagonal of a rhombus when the area is 48 and the other diagonal is 12.

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Question 626310: Find the length of a diagonal of a rhombus when the area is 48 and the other diagonal is 12.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Find the length of a diagonal of a rhombus when the area is 48 and the other diagonal is 12.
Let the rhombus be ABCD with diagonal AC given = 12, and we are
to find the length of diagonal BD:



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%2F2base×height

                  24 = 1%2F2BD·AE
                  24 = 1%2F2BD·6
                  24 = 3·BD
                   8 = BD

Edwin