Question

ABCD is a rhombus whose diagonals AC and BD intersect at a point O. If side AB$=10$ cm and diagonal BD$=16$ cm, find the length of diagonal AC.

Answer 1

According to quesion,
$AB=10$, $BD=16$
From figure,
$AO+OC=AC$
& $AO=OC$
=> $2AO=AC$
In $△AOB$, from pythagorous
$A{B}^2=A{O}^2+B{O}^2$
=> $100=64+A{O}^2$
=> $AO=6$
Since, $AC=2OA$,
Hence, $AC=12$cm