Question

Each side of a rhombus is 13 cm and one diagonal is 10 cm.Find : the length of its other diagonal

Answer 1

hope this helps......

Answer 2

the rhombus ABCD ( let be the name )
GIVEN-
each sides of rhombus = 13 cm
one diagonal AC = 10 cm

draw another diagonal BD
as we know that the diagonals of rhombus bisect each other at 90 degree.
so O is the point in which the diagonals bisect.
So AO = OC = 5cm
and BO = OD
now,
triangle AOD is right angle triangle
triangle DOC is right angle triangle
triangle COB is right angle triangle
triangle BOA is right angle triangle

(we can take any one )

AOD
= (AO)^2 + (OD)^2 = AD^2
= (5)^2 + (OD)^2 = 13^2
= 25 + (OD) ^2 = 169
= (OD)^2 = 169-25
= (OD)^2 = 144
= OD =√144
= OD = 12

as BO = OD,
and BO = 12cm than OD also = 12cm
now diagonal AC = BO +OD
AC = 12 + 12
AC = 24 cm.