Question

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

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

Answer 1

The correct option is C

8 cm

Figure 13.

Diagonals of a rhombus bisect each other at right angle.

Let BD = 6cm
$\Rightarrow$ $BE=\frac{BD}{2}$
= 6/2 = 3cm
In $\Delta$ AEB,
By applying Pythagoras Theorem

$A{B}^2=B{E}^2+A{E}^2$
$A{E}^2=A{B}^2-B{E}^2$
$A{E}^2=5^2-3^2$
$A{E}^2=25-9$
$A{E}^2=16$
$AE=4$
As, AC = 2AE
AC = 2x4
= 8 cm