the diagnals of a rhombus meaasure 16cm and 30cm.find its perimeter
Given ABCD is a rhombus with diagonal AC = 30cm and BD = 16cm.
we know that diagonals of a rhombus bisect each other at right angle.
Now In ΔAOB, right angle at O.
Apply pythagorus theorem
(AB)2 = (OA)2 + (OB)2
(AB)2 = (15)2 + (8)2
(AB)2 = 225 + 64
(AB)2 = 289
AB = 17 cm
Now all sides of rhombus are equal
∴AB = BC = CD = DA = 17 cm.
Perimeter of rhombus ABCD = 4 × side
= 4 × AB
= 4 × 17
= 68 cm