Rhombus ABCD has an area of 264 square units. If DB=12 units find AC.

Question

So far this is what I have-
1/2(264)=132 132/2=66
66-12=44units
Is this the correct process?

Answer 1

I don't follow your work.

Sketch the rhombas. One diagonal is 12, so half that diagonal is 6.

call that half b, so 2b=12
now call half the other diagonal a
so the length of that diagonal is 2a, and that is what you are looking for.

Now, the diagonals of a rhombus are perpendicular bisectors, so you have four right triangles, the area of which is
1/2 a b=264/4
or ab=132, but a=6, so a=22
which means 2a=44, so your answer is correct.