PQRS is a square, M is the mid-point of PQ and N is a point on QR such that NR is two-third of QR. If the area of ΔMQN is $$48cm^2$$ , then what is the length (in cm) of PR ?

Given : PQRS is a square and PM = MQ and NQ = $$\frac{1}{3}$$ QR

To find : PR = ?

Solution : Let the side of square = $$6x$$ cm

=> MQ = $$\frac{6x}{2}=3x$$ cm and NQ = $$\frac{6x}{3}=2x$$ cm

Area of ΔMQN = $$\frac{1}{2}\times(MQ)\times(NQ)=48$$

=> $$3x\times2x=48\times2=96$$

=> $$x^2=\frac{96}{6}=16$$

=> $$x=\sqrt{16}=4$$ cm

Thus, side of square = $$6\times4=24$$ cm

$$\therefore$$ Diagonal PR = $$\sqrt{(24)^2+(24)^2}=24\sqrt2$$ cm

=> Ans - (D)