Question

each side of a rhombus is 10 cm long and one of its diagonal measure 16 cm. the length of the other diagonal is

Answer 1

In rhombus abcd, ab=bc=cd=da=10cm (given)

one of its diagonal is 16cm
mark the point of intersection as P
now,dp=bp (diagonals of a rhombus bisect each other)

by pythagoras theorem

ap²+bp²=ab²
9²+bp²=10²
bp²=10²-9²
bp²=100-81
bp²=19
bp=√19
bp=4.35

∴bp=4.35
∴db=dp+bp

∵dp=bp
⇒db=4.35+4.35
       =8.7

hope helped u