Question

Two diagonals of a rhombus are 72 cm and 30 cm respectively. what is its perimeter?

Answer 1

Hi ,

Given a rhombus you can directly find the perimeter using its :
1. Side : 4a
2. Diagonals(d1,d2): 2(sqrt(d1^2+d2^2))

here
d1=72
d2=30
 so
perimeter = 2 ( sqrt( 72^2 + 30^2 ) )
= 2*sqrt(6084)
=2*78
= 156 square cm

Hope it helped.
Please let me know if any further doubt.
Cheers !!!

Answer 2

diagonals of a rhombus split the rhombus into 4 equal triangles, each with base and height half that of the diagonal. Hypotenuse of this triangle is one side of the triangle, lets call it XX.

Applying pythagoras theorem,

X2=362+152X2=362+152

X2=32(122+52)X2=32(122+52)

X2=32(169)X2=32(169)

X2=32∗132X2=32∗132

X=3∗13=39.X=3∗13=39.

Perimeter would be 4 times XX

4∗39=156
hope it helps