• # question_answer The area of a rectangle lies between 40$\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}$ and 45$\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}$. If one of the sides is 5cm, then its diagonal lies between A)  8 cm and 10 cm        B)  9 cm and 11 cmC)  10 cm and 12 cm         D)  11 cm and 13 cm

(b):- Area of rectangle lies between 40$c{{m}^{2}}$ and 45$c{{m}^{2}}$ Now one side = 5 cm Since, area cannot be less than 40$c{{m}^{2}}$ $\therefore$Other side cannot be less than $=\frac{40}{5}=8$ cm Since, area cannot be greater than 45$c{{m}^{2}}$ $\therefore$Other side cannot be greater than $=\frac{45}{5}=9$cm $\therefore$Minimum value of diagonal $=\sqrt{{{8}^{2}}+{{5}^{2}}}$ Maximum value of diagonal $=\sqrt{{{9}^{2}}+{{5}^{2}}}$                                          $=\sqrt{106}=10.3$cm So, diagonal lies between 9 cm and 11 cm