Question

Construct a rhombus PQRS, where PQ is 6 cm and PR = 8 cm. What is the measure of QS.

Answer 1

We know that, sides of rhombus are equal.

So, $PQ=QR=RS=PS=6cm$

$\Rightarrow$ Draw a line segment $PQ=6cm$

$\Rightarrow$ Take $P$ as center with radius $8cm$ and draw an arc.

$\Rightarrow$ Take $Q$ as center with radius $6cm$ and draw an arc, which meets previous arc at point $R$.

$\Rightarrow$ Take $P$ as center with radius $6cm$ and draw an arc.

$\Rightarrow$ Take $R$ as center with radius $6cm$ and draw an arc, which meets previous arc at point $S$.

$\Rightarrow$ Join $QR,RS,SP,PR$ and $QS$

$\therefore$ $PQRS$ is a required rhombus.

$\Rightarrow$ Measure the length of $QS$.

We get $QS=8.9cm$