Question

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

Answer 1

$\huge\fbox{\fbox{\fbox{\pink{\underline{Answer}}}}}$

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.