Question

The perimeter of a rhombus is $40$ cm. If one diagonal is $16$ cm. Find the value of its another diagonal.

Answer 1

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 $=16cm$, then OP $=8cm$, OQ $=\frac{SQ}{2}$
Since, triangle POQ is a right angled triangle,
${PQ}^2={OP}^2+{OQ}^2$
${10}^2=8^2+{\left(\frac{SQ}{2}\right)}^2$
${\left(\frac{SQ}{2}\right)}^2={10}^2-8^2$
$\left(\frac{SQ}{2}\right)=\sqrt{36}=6cm$
$SQ=12cm$
Hence, length of the other diagonal $=12cm$