Question

The perimeter of a rhombus is 40 cm. If the length of one of its diagonals is 12 cm, what is the length of the other diagonal ?

• A. $16$ cm
• B. $8$ cm
• C. $20$ cm
• D. $10$ cm

Answer 1

The correct option is A $16$ cm

Let PQRS be the rhombus as shown in the figure.
Since the length of all sides of a rhombus are equal, Perimeter $=4\times$ length of one side $=>4\times PQ=40cm=>PQ=10cm$
Hence, length of each side of the rhombus $=10cm$
In a rhombus, the diagonals bisect each other at ${90}^0$
Referring the diagram, if PR $=12cm$, then OP $=6cm$, OQ $=\frac{SQ}{2}$
Since, triangle POQ is a right angled triangle,
${PQ}^2={OP}^2+{OQ}^2$
${10}^2=6^2+{\left(\frac{SQ}{2}\right)}^2$
${\left(\frac{SQ}{2}\right)}^2={10}^2-6^2$
$\left(\frac{SQ}{2}\right)=\sqrt{64}=8cm$
$SQ=16cm$
Hence, length of the other diagonal $=16cm$