Question

In the rhombus ABCD, AC and BD are the diagonals. If the diagonals are 24 cm and 10 cm. Find the length of each of its sides.

• A. 13 cm
• B. 12 cm
• C. 5 cm
• D. 10 cm

Answer 1

The correct option is A 13 cm

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

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

$OA=\frac{AC}{2}=\frac{24}{2}=12cm$

$OB=\frac{BD}{2}=\frac{10}{2}=5cm$

Now, in $△AOB,\angle AOB={90}^o$

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

$\Rightarrow$ $(AB{)}^2=(12{)}^2+(5{)}^2$

$\Rightarrow$ $(AB{)}^2=144+25$

$\Rightarrow$ $(AB{)}^2=169$

$\therefore$ $AB=13cm$

We know that, all sides of rhombus are equal.

$\therefore$ The length of each side of rhombus is $13cm$