Directions: Each of these questions contains two statements: |
Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
Assertion [A] In \[\Delta ABC\], \[\angle B=90{}^\circ \] and \[BD\bot AC\]. If AD = 4 cm and CD = 5 cm, then BD is \[2\sqrt{5}\] cm. |
Reason [R] If a line divides any two sides of a triangle in the same ratio, then the line must not be parallel to the third side. |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is False.
D) A is false; R is true.
Correct Answer: C
Solution :
\[\Delta ABC\] is similar to \[\Delta ADB\] |
\[\therefore \,\,\,\frac{AB}{AD}=\frac{AC}{AB}\] |
\[A{{B}^{2}}=AD\times AC\] |
\[A{{B}^{2}}=4\times 9\] |
AB = 6 cm |
In \[\Delta ADB,\] \[A{{B}^{2}}=A{{D}^{2}}+B{{D}^{2}}\] |
\[36\text{ }=\text{ }16\text{ }+\text{ }B{{D}^{2}}\] |
\[B{{D}^{2}}\text{ }=\text{ }20\] |
\[BD=2\sqrt{5}\,cm\] |
Hence, Statement I is true and Statement II is false. |
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