Question

the diagonals of a rhombus are 16 cm and 30 cm .find the length of the side of the rhombus​

Answer 1

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Side of Rhombus = 17 cm

Step-by-step explanation:

Let the diagonals be AC and BD.

AC = 16 cm

BD = 30 cm

Since, diagonals of a rhombus bisect each other. Let the diagonals bisect at point O.

Therefore,

AO = OC = 8 cm

OB = OD = 15 cm

Therefore, we have four small right angled triangles in the rhomus.

In $\triangle$ AOB , we have:

AO as base , OB as perpendicular and AB as hypotenuse.

We have to calculate AB.

Applying Pythagoras Theorem, we get:

$\sf AB^2=OA^2+OB^2\\ \sf AB^2=8^2+15^2\\\sf AB^2 = 289 cm^2\\\sf AB = \sqrt{289 cm^2}\\\sf AB = 17 cm$

Since, all sides of rhombus are equal. So, length of side of rhombus is 17 cm.

Answer 2

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

and 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

Since all the sides of the rhoumbus are congruent

Hence of the side of the rhoumbus is 17cm