Question

$\text{In square PQRS :}\left(i\right)ifPQ=3x-7andQR=x+3;findPS\left(ii\right)ifPR=5xandQR=9x-8.FindQS$

Answer 1

$\left(i\right)\because \text{sides of square are equal.}$

$\therefore PQ=QR\Rightarrow 3x-7=x+33x-x=3+7\Rightarrow 2x=10x=5\therefore PS=PQ=3x-7=3\times 5-7=8$

$\left(ii\right)PR=5xandQS=9x-8$

$\text{As diagonals of square are equal.}\therefore PR=QS5x=9x-8\Rightarrow 5x-9x=-8-4x=-8\Rightarrow x=2\therefore QS=9x-8=9\times 2-8=10$