Question

Question 8
The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

Answer 1

Given: Diagonals AC = 30 cm and DB = 16cm.
Since the diagonals of the rhombus bisect at right angle to each other.

$Therefore,OD=\frac{DB}{2}=\frac{16}{2}=8cmAnd,OC=\frac{AC}{2}=\frac{30}{2}=15cm\text{Now,In right angle triangle DOC,}(DC{)}^2=(OD{)}^2+(OC{)}^2\Rightarrow (DC{)}^2=(8{)}^2+)(15{)}^2\Rightarrow (DC{)}^2=64+225=289\Rightarrow DC=\sqrt{289}=17cm\text{Perimeter of rhombus}=4\times side=4\times 17=68cm\text{Thus, the perimeter of rhombus is 68cm.}$