Question 8
The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.
Given: Diagonals AC = 30 cm and DB = 16cm.
Since the diagonals of the rhombus bisect at right angle to each other.
Therefore, OD=DB2=162=8 cmAnd, OC=AC2=302=15 cm
Now, in right angle triangle DOC,
(DC)2=(OD)2+(OC)2⇒(DC)2=(8)2+)(15)2⇒(DC)2=64+225=289⇒DC=√289=17 cm
Perimeter of rhombus = 4×side
=4×17=68 cm
Thus, the perimeter of rhombus is 68cm.