Question

.The diagonals of a rhornbus measure 16 cm and 30 cm. Find its perimeter​

Answer 1

Step-by-step explanation:

And we all know that the diagonals of the rhombus bisect each other at 90 degrees. And ∠AOD=∠AOB=∠BOC=∠COD=90o as shown in the above figure. Now it is given that the diagonals of the rhombus are 16 cm and 30 cm. Therefore, AC = 30cm and BD = 16cm.

Answer 2

Step-by-step explanation:

.Let PQRS be a rhombus, all sides of rhombus has equal length and its diagonal PR and SQ are intersecting each other at a point O. Diagonals in rhombus bisect each other at 90° .

So, PO = (PR/2)

= 16/2

= 8 cm

And, SO = (SQ/2)

= 30/2

= 15 cm

Then, consider the triangle POS and apply the Pythagoras Theorem,

PS² = PO²+ SO²

PS² = 82 + 152

PS² = 64 + 225

PS²= 289

PS = √289

PS = 17 cm

Hence, the length of side of rhombus is 17 cm

Now,

Perimeter of Rhombus = 4 × Side of the Rhombus

= 4 × 17

= 68 cm

∴ Perimeter of Rhombus is 68 cm.PS2 = 289

PS = √289

PS = 17 cm

Hence, the length of side of rhombus is 17 cm

Now,

Perimeter of rhombus = 4 × side of the rhombus

= 4 × 17

= 68 cm

∴ Perimeter of rhombus is 68 cm.