Question

ABCD is a rhombus whose diagonals intersect at 0. If AB = 10 cm, diagonal BD = 16 cm, find the length of diagonal AC.

Answer 1

In rhombus ABCD.

AB = 10 cm, diagonal BD = 16 cm.
Draw diagonal AC which bisects BD at O at right angle.
$\therefore$ BO = OD = 8 cm and AO = OC.
ow in $\Delta AOB$,
$A{B}^2=A{O}^2+B{O}^2$
$(10{)}^2=A{O}^2+(8{)}^2\Rightarrow 100=A{O}^2-64\Rightarrow A{O}^2=100-64=36=(6{)}^2\therefore AO=6\therefore AC=2AO=2\times 6=12cm$