Question

Lal is constructing a rectangle PQRS. The length of the diagonal is $6cm$ and the length of the sides are $3cm$ and $4cm$. Is the construction of the rectangle PQRS possible?

• A. Yes
• B. No
• C. Yes, if the diagonal measures 5 cm.
• D. Even, the changes in the length of the diagonal is not sufficient.

Answer 1

The correct option is C Yes, if the diagonal measures 5 cm.

The construction is not possible with the given measurements.

Since it is a rectangle, all the angles will be 90°. Hence, PR will be one of the diagonal.

If we consider PQR to be a triangle, right angled at Q, then by Pythagoras Theorem, $P{Q}^2+Q{R}^2=P{R}^2$...(i)
$\Rightarrow P{Q}^2+Q{R}^2=4^2+3^2$
$=16+9=25.$

Now, from (i), $P{R}^2=25$
Then, $PR=\sqrt{25}=5cm.$


So if PR is of length $5cm$ instead of $6cm$, then the construction of rectangle PQRS will be possible.