Question

What is the length of the other diagonal of the rhombus when area is 84 sqcm and one of its diagonals is 14 cm

Answer 1

area of rhombus =p*k/2
P and K are diagonals

84=14*k/2=
42=14×k
21=7×k
3=k

Answer 2

The area of a regular rhombus is A=pq/2A=pq/2, where p and q are the diagonals of the shape.

given A = 24 and p = 14

24=14q/224=14q/2

48=14q48=14q

q=22q=22

so the other diagonal is 22 cm long.

now, by Pythagorean theorem, each side of the rhombus (annotate as s) is given by:

s2=(p/2)2+(q/2)2s2=(p/2)2+(q/2)2

s2=(14/2)2+(22/2)2s2=(4/2)2+(22/2)2

s2=14+56s2=14+56

s2=70s2=70

s=210−−√s=210

since there are 4 sides in a rhombus, so the perimeter of it is:

4∗210−−√4∗210

=810−−√