Question

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

Answer 1

We know that the diagonals of a rhombus bisect each other at right angles.
∴ BO=$\frac{1}{2}$BD=$(\frac{1}{2}\times 16)$ cm=8cm
AB=10 cm and ∠AOB=90°
From right ∆OAB:
$A{B}^2=A{O}^2+B{O}^2$
$\Rightarrow A{O}^2=(A{B}^2–B{O}^2)$
$\Rightarrow A{O}^2=(10{)}^2-(8{)}^{2}c{m}^2$
$\Rightarrow A{O}^2=(100-64)c{m}^2$
$=36c{m}^2$
$\Rightarrow AO=\sqrt{36}cm=6cm$
∴ $AC=2\times AO=(2\times 6)cm=12cm$