question_answer

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

A) \[5.6\,\,cm\]

B) \[5.8\,\,cm\]

C) \[6.0\,\,cm\]                  

D) \[6.2\,\,cm\]

Correct Answer: A

Solution :

For similar triangles, ratio of areas is equal to the ratio of the squares of any two corresponding sides.

Here, \[\frac{\text{area}\,\,\text{of}\,\,\Delta ABC}{\text{area}\,\,\text{of}\,\,\Delta \text{XYZ}}=\frac{A{{B}^{2}}}{X{{Y}^{2}}}\]

\[\Rightarrow \]   \[\frac{32}{60.5}=\frac{A{{B}^{2}}}{{{(7.7)}^{2}}}\]

\[\Rightarrow \]   \[\frac{32\times 59.29}{60.5}=A{{B}^{2}}\]

\[\Rightarrow \]   \[31.36=A{{B}^{2}}\]

\[\therefore \]      \[AB=\sqrt{31.36}=5.6\,\,cm\]