Question

The diagonals of a rhombus are $32cm$ and $24cm$, respectively. The perimeter of the rhombus is

• A. $80cm$
• B. $72cm$
• C. $68cm$
• D. $88cm$

Answer 1

Answer: (A)

$80cm$

In a rhombus, the diagonals bisect each other at ${90}^0$.

Referring the diagram, if $PR=32cm,SQ=24cm$, then $OP=16cm,OQ=12cm$

Since $△POQ$ is a right angled triangle,

${PQ}^2={OP}^2+{OQ}^2=>{16}^2+{12}^2=400$

$PQ=\sqrt{400}=20cm$

Hence, the length of the sides of the rhombus $=20cm$.

Since the length of all sides of a rhombus are equal,

Perimeter $=4\times$ length of one side $=4\times 20=80cm$