| In the given figure, if\[\angle ADE=\angle B\], and AD = 6.8 cm, AE = 8.6 cm, BE = 2.4 cm and BC = 55 cm, then the value of DE is |
 |
A) 6.8cm
B) 2.4cm
C) 3.4cm
D) 4.8cm
Correct Answer: C
Solution :
| In \[\Delta ADE\] and \[\Delta ABC\], |
| \[\angle ADE=\angle B\] [given] |
| and \[\angle A=\angle A\] [common] |
| \[\Delta ADE\tilde{\ }\Delta ABC\] [by AA corollary] |
| \[\therefore \,\,\,\frac{AD}{AE+EB}=\frac{DE}{BC}\] |
| [sides of similar triangles are proportional] |
| \[\Rightarrow \,\,\,\frac{AD}{AE+EB}=\frac{DE}{BC}\] |
| \[\Rightarrow \,\,\,\frac{6.8}{8.6+2.4}=\frac{DE}{5.5}\] |
| \[\Rightarrow \,\,\,DE=\frac{6.8\times 5.5}{8.6+2.4}\,cm\,=3.4\,\,cm\] |
| Hence, DE = 3.4 cm |
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