Question

the diagonals of a rhombus measure 16 cm and 30 cm  .find its perimeter    ( in easy way)?

Answer 1

given,the measures of diagonals16,30
We know that diagonals of rhombus are perpendicular bisectors of each other.

db=16
DO=DB/2
DO=16/2
DO=8cm
similarly,AO=15cm
by using pythogaras theorem,
DO²+AO²=DA²
8²+15²=DA²
64+225=DA²
289=DA²
DA=17
perimeter=DA×4
              =17×4
PEIMETER=68CM

Answer 2

now by seeing this attached picture we can say that 8 cm +8 cm = 16 cm and 15 cm + 15 cm = 30 cm...
since diagonal of a rhombus bisects each other
now by applying Pythagoras theorem we get,
h² = p² + b²
h² = 8² + 15²
h² = 64 + 225
h² = 289
h = √289
h = 17
therefore perimeter of the rhombus , 
= 4 * side
= 4 * 17
= 68 cm
therefore perimeter of the rhombus = 68 cm
   i hope that my answer will help u.................................^_^