| In the given figure P and Q are points on sides AB and A C respectively of \[\Delta ABC\]such that AP = 35 cm, PB =7 cm, AQ = 3 cm and QC = 6 cm. |
| If PQ = 45 cm, then the value of BC is |
 |
A) 13.5cm
B) 3.4 cm
C) 2.6cm
D) 1.6cm
Correct Answer: A
Solution :
| In the given figure,\[\frac{AQ}{AC}=\frac{AP}{AB}=\frac{1}{3}\] |
| Therefore, by converse of basic proportionality theorem, we have |
| \[QP\,\,\,|\,\,|\,\,\,CB\] |
| Hence, \[\Delta AQP\tilde{\ }\Delta ACB\] |
| \[\frac{AQ}{AC}=\frac{AP}{AB}=\frac{QP}{CB}\] |
| \[\Rightarrow \frac{1}{3}=\frac{4.5}{BC}\] |
| \[BC=13.5\,\,\,cm\] |
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