Question

In square $PQRS$,
(i). If $PQ=3y-7$ and $QR=y+3$,find $PS$
(ii) If $PR=5x$ and $QS=9x-8$. Find $QS$

Answer 1

Part (i) In a square all sides are equal,

so we have $PQ=QR$

$\Rightarrow 3y-7=y+3$

$\Rightarrow 3y-y=3+7$

$\Rightarrow 2y=10$

$\Rightarrow y=5$

$\Rightarrow PS=3y-7=15-7=8$

$PS=8$

Part (ii) In A square both the diagonals are of equal length

so we have

$PR=QS$

$\Rightarrow 5x=9x-8$

$\Rightarrow 8=4x$

$\Rightarrow x=2$

$\Rightarrow QS=9x-8=18-8$

$QS=10$