Question

If the diagonals of a rhombus are $18cm$ and $24cm$ respectively, then its side is equal to

• A. 16 cm
• B. 15 cm
• C. 20 cm
• D. 17 cm

Answer 1

Answer: (B)

$\left(15cm\right)$

Given, diagonals of a rhombus are $18cm$ and $24cm$.

We know that the diagonals of a rhombus bisect each other at right angles.

$\therefore AO=OC=\frac{24}{2}=12cm$
$BO=OD=\frac{18}{2}=9cm$
Consider right-angled triangle $\Delta AOB$,
From pythagoras theorem, we have
$A{B}^2=A{O}^2+B{O}^2$
$=(12{)}^2+(9{)}^2$
$=144+81$
$\Rightarrow A{B}^2=225$
$\Rightarrow AB=\sqrt{(15{)}^2}$
$\therefore AB=15cm$
Hence, the measure of each side of given rhombus is $=15cm$