Question

The diagonals of a rhombus measure 16cm and 30cm. Find the perimeter.

Answer 1

Diagonals of perimeter are perpendicular to each other . So ,we can use Pythagorean theorem to find the side length of rhombus .
Diagonal = 16/2 = 8cm
Diagonal = 30/2 = 15cm

82+152 = s2
64+225 = 289 = s2
Side length(s) = 17

Perimeter of rhombus = 4*17 = 68 cm

Answer 2

Answer :

The perimeter of the rhombus is 68 cm.

Step-by-step explanation :

Given, diagonal of rhombus = 16 cm & 30 cm

Since, we know that diagonals of a rhombus bisect each other.

Therefore,

First diagonal, p = 8 cm

Second diagonal, q = 15 cm

Now, by Pythagoras Theorem,

$\implies h^{2}=p^{2}+b^{2}$

$\implies h^{2}=8^{2}+15^{2}$

$\implies h^{2}=64+225$

$\implies h^{2}=289$

$\implies h=\sqrt{289}$

$\implies h=17$

So, the side of the the rhombus is 17 cm.

Now, perimeter -

$\implies 4\times side$

$\implies 4\times 17$

$\implies 68$ cm