Question

The diagonal of a rhombus measure $16$ cm and $30$ cm . Find its perimeter.

Answer 1

Some of the properties of Rhombus are :

a. All sides are equal

b. The diagonals bisect each other at

Let us assume that we have a rhombus $ABCD$, such that the diagonals $AC$ and $BD$ bisects each other.

Now, we know that

$AO=OC=$$\frac{1}{2}AC=\frac{1}{2}\times 16=8\text{cm}$

Similarly,

$BO=OD=15\text{cm}$

Now since, $△AOD$ is a right angled triangle.

Therefore, $AD=\sqrt{A{O}^2+O{D}^2}$

$=\sqrt{8^2+{15}^2}$

$=\sqrt{64+225}$

$AD=\sqrt{289}=17\text{cm}$

Perimeter of Rhombus, $P=4a$, where $a$ is the length of one of the side.

$P=4\times a$

$P=4\times 17$

$P=68\text{cm}$