Question

In the rhombus ABCD, AC and BD are the diagonals. If the diagonals are 16 cm and 12 cm. Find the length of each of its sides.

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

Answer 1

Answer: (A)

10 cm

We know that, diagonals in a rhombus bisect each other perpendicularly.

Let $O$ is the intersecting point of diagonals $AC$ and $BD$.

$OA=\frac{AC}{2}=\frac{16}{2}=8cm$

$OB=\frac{BD}{2}=\frac{12}{2}=6cm$

Now, in $△AOB,\angle AOB={90}^o$

$\Rightarrow$ $(AB{)}^2=(OA{)}^2+(OB{)}^2$ [ By Pythagoras theorem ]

$\Rightarrow$ $(AB{)}^2=(8{)}^2+(6{)}^2$

$\Rightarrow$ $(AB{)}^2=64+36$

$\Rightarrow$ $(AB{)}^2=100$

$\therefore$ $AB=10cm$

We know that, all sides of rhombus are equal.

$\therefore$ The length of each side of rhombus is $10cm$