Question

In given figure PQRS is a rectangle with sides $PS=5cm$ and $PQ=12cm$. Find the length of QR, SR and the two diagonals PR and QS

• A. $QR=5cm,SR=12cm,PR=QS=13cm$
• B. $QR=5cm,SR=12cm,PR=QS=12cm$
• C. $QR=12cm,SR=5cm,PR=QS=13cm$
• D. none of the above

Answer 1

The correct option is A $QR=5cm,SR=12cm,PR=QS=13cm$

PQRS is a given rectangle Sides of rectangle $PS=5cm$ and $PQ=12cm$(Given)

Since opposite sides of rectangle are equal

$\Rightarrow PQ=SR=12cm$

$\Rightarrow PS=QR=5cm$

In rectangle all the angles are right angles

Hence length of diagonal =$\sqrt{l^2+b^2}$

Now in $△PQR$

using Pythagoras theorem, we have

${PR}^2={PQ}^2+{QR}^2$

$\Rightarrow PR=\sqrt{{12}^2+5^2}$

$\Rightarrow PR=\sqrt{144+25}$

$\Rightarrow PR=\sqrt{169}=13$

Hence length of diagonal $PR=13cm$

Similarly length of diagonal $QS=13cm$