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, \[\frac{\text{area}\,\,\text{of}\,\,\Delta ABC}{\text{area}\,\,\text{of}\,\,\Delta \text{XYZ}}=\frac{A{{B}^{2}}}{X{{Y}^{2}}}\] |
\[\Rightarrow \] \[\frac{32}{60.5}=\frac{A{{B}^{2}}}{{{(7.7)}^{2}}}\] |
\[\Rightarrow \] \[\frac{32\times 59.29}{60.5}=A{{B}^{2}}\] |
\[\Rightarrow \] \[31.36=A{{B}^{2}}\] |
\[\therefore \] \[AB=\sqrt{31.36}=5.6\,\,cm\] |
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