| Assertion (A): In \[\Delta ABC,\] \[\left. DE \right\|BC\] such that \[AD=(7x-4)cm,\] \[AE=(5x-2)cm,\] \[DB=(3x+4)cm\] and \[\text{EC}=\text{3x cm}\] then x equal to 5. |
| Reason (R): If a line is drawn parallel to one side of triangle to intersect the other two sides at a distant point, then the other two sides are divided in the same ratio. |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: D
Solution :
| [d] Assertion is false but reason is true. |
| We have, \[\frac{AD}{DB}=\frac{AE}{EC}\] |
| \[\frac{7x-4}{3x+4}=\frac{5x-2}{3x}\] |
| \[21{{x}^{2}}-12x=15{{x}^{2}}+20x-6x-8\] |
| \[6{{x}^{2}}-26x+8=0\] |
| \[3{{x}^{2}}-13x+4=0\] |
| \[3{{x}^{2}}-12x-x+4=0\] |
| \[3x(x-4)-1(x-4)=0\] |
| \[(x-4)\,(3x-1)=0\] |
| \[x=4,\,\,\frac{1}{3}\] |
| So, assertion is incorrect but reason is correct. |
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