| If \[\Delta ABC\tilde{\ }\Delta PQR,\], then \[y+z\] equals: |
 |
A) \[2+\sqrt{3}\]
B) \[4+3\sqrt{3}\]
C) \[4+\sqrt{3}\]
D) \[3+4\sqrt{3}\]
Correct Answer: B
Solution :
| [b] Given. \[\Delta ABC\tilde{\ }\Delta PQR\] |
| \[\therefore \,\,\,\,\,\,\,\,\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CA}{RP}\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\,\,\,\frac{z}{3}=\frac{8}{6}=\frac{4\sqrt{3}}{y}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\frac{z}{3}=\frac{8}{6}\] and \[\frac{8}{6}=\frac{4\sqrt{3}}{y}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,z=\frac{24}{6}=4\]and \[y=\frac{24\sqrt{3}}{8}=3\sqrt{3}\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y+z=4+3\sqrt{3}.\] |
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