question_answer

ABC and XYZ are two similar triangles with\[~\angle C=\angle Z\], whose areas are respectively \[32c{{m}^{2}}\]and\[60.5c{{m}^{2}}\]. If XY = 7.7 cm, then AB is equal to-

A) 5.6 cm                         

B) 5.8 cm

C) 6.0 cm                         

D) 6.2 cm

Correct Answer: A

Solution :

For any two similar triangles, ratio of areas is equal to the ratio of the squares of any two corresponding sides.             Hence, \[\frac{area\,\,of\,\,\Delta ABC}{area\,\,of\Delta XYZ}=\frac{A{{B}^{2}}}{X{{Y}^{2}}}\] \[\Rightarrow \,\,\,\,\,\,\,\frac{32}{60.5}=\frac{A{{B}^{2}}}{{{(7.7)}^{2}}}\] \[\Rightarrow \,\,\,\,\,\,\,\frac{32\times 59.29}{60.5}=A{{B}^{2}}\Rightarrow 31.36=A{{B}^{2}}\] \[\therefore \,\,\,\,\,\,AB=\,\sqrt{31.36}=\mathbf{5}.\mathbf{6}\text{ }\mathbf{cm}\]