Question

If the length of two diagonals of rhombus are 16 cm and 30 cm, find the area and the length of the side of the rhombus.​

Answer 1

Step-by-step explanation:

$\huge\bf\underline{Given:}$

=>The length of two diagonals of rhombus are 16 cm and 30cm.

$\huge\bf\underline{To \: Find: }$

=>The area and the length of the side of the rhombus.

$\huge\bf\underline{Solution:}$

Let ABCD is a rhombus

=>AB,BC,CD,AD are the sides of the rhombus and

AC and BD are the diagonals of the rhombus

Where

AC= 30

BD=16

=>O is the point where daigonals are bisect each other.

=> As we know the property of rhombus that daigonals are bisect each other then

AO=CO=15

BO=OD=8

=>Since diagonals are perpendicular to each other then we can apply Pythagoras theoram on it,

=>By applying Pythagoras theoram on ∆AOD

AD^2=A0^2+OD^2

AD^2=15^2+8^2

AD^2=289

AD=17.

$\huge\bf\underline{Answer}$

Therefore, all the sides of the rhoumbus are congruent

Hence of the side of the rhoumbus is 17cm.