Question

The length of the diagonals of a rhombus are $16cm$ and $12cm.$ The length of each side of the rhombus is

• A. $8cm$
• B. $9cm$
• C. $10cm$
• D. $12cm$

Answer 1

Answer: (C)

$10cm$

Let $ABCD$ be rhombus with $AC$ and $BD$ daigonals.
Let $AC$ and $BD$ bisect at $O$.
Therefore $AO=16/2=8$
$BO=12/2=6cm$
In right angled triangle $AOB$, by Pythagoras theorem we can write as
$A{B}^2=A{O}^2+O{B}^2$
$A{B}^2=8^2+6^2$
$A{B}^2=64+36$
$AB=100$
$AB=10$
Length of rhombus is $10cm$