Question

If the length of one of the diagonals of a rhombus of side 20 cm is 24 cm, then the length of the other diagonal is :

• A. 16 cm
• B. 32 cm
• C. 24 cm
• D. 12 cm

Answer 1

The correct option is B

32 cm

Given, the length of each side is 20 cm.
So, AB = BC = CD = AD = 20 cm.

Also, the length of one diagonal (say) AC is given as 24 cm.

We know that in a rhombus, diagonals bisect each other at ${90}^{\circ }$ .

Therefore,

$AO=OC=\frac{1}{2}\left(AC\right)=\frac{1}{2}\times 24=12cm...\left(1\right)$

Now in triangle AOB, $\angle BOA={90}^{\circ }$

Applying Pythagoras theorem,
we get,

$A{B}^2=O{A}^2+O{B}^2{20}^2=(12{)}^2+O{B}^2\text{from (1)}O{B}^2={20}^2-{12}^2=400-144=256OB=16cm$
$\text{Now}OB=OD=\frac{1}{2}\times BD\Rightarrow BD=2\left(OB\right)=32cm$

Hence, the length of other diagonal BD = 32 cm.