Question

$ABCD$ is a rhombus. If its side and one diagonal measure $5cm$ and $6cm$ respectively, the measure of its other diagonal is

• A. 6 cm
• B. 12 cm
• C. 8 cm
• D. 10 cm

Answer 1

The correct option is C 8 cm

Diagonals of a rhombus bisect each other at right angle.

Let $BD=6cm\Rightarrow BE=\frac{BD}{2}$
In $\Delta AEB,$

$A{B}^2=B{E}^2+A{E}^2$
$\Rightarrow B{E}^2=A{B}^2-A{E}^2$
$\Rightarrow B{E}^2=5^2-3^2$
$\Rightarrow B{E}^2=25-9$
$\Rightarrow BE=4cm$
$\because BD=2BE$
$\therefore BD=8cm$