Question

In a rhombus $ABCD$, the diagonals intersect at $O$. If $AB=10cm$, diagonal $BD=16cm$, then the length of the diagonal $AC$ is _______.

• A. $12cm$
• B. $6cm$
• C. $16cm$
• D. $8cm$

Answer 1

The correct option is A $12cm$

In a rhombus, diagonals bisect each other at ${90}^{\circ }$

$\therefore BO=\frac{1}{2}BD=8cm$

$\angle AOB={90}^{\circ }$

$\therefore$ In $△AOB$,

$A{B}^2=A{O}^2+B{O}^2$

$\therefore {10}^2=A{O}^2+8^2$

$\Rightarrow AO=6cm$

$AC=2\times AO=12cm$