Consider the triangle shown in the figure where BC = 12 cm, DB = 9 cm, CD = 6 cm and ∠BCD = ∠BAC. What is the ratio of the perimeter of the triangle ADC to that of the triangle BDC ?
A. 7 : 9
B. 8 : 9
C. 6 :9
D. 5 : 9
E. None of these
Answer: Option A
Solution(By Examveda Team)
Here, ∠ACB = c + 180 - (2c - b) = 180 - (b + c) So, We can say that ΔBCD and ΔABC will be similar. According to property of similarity, $$\frac{{{\text{AB}}}}{{12}} = \frac{{12}}{9}$$ Hence, AB = 16 $$\frac{{{\text{AC}}}}{6} = \frac{{12}}{9}$$ AC = 8 Hence, AD = 7 and AC = 8 Now, $$\eqalign{ & \frac{{{\text{Perimeter of Delta ADC}}}}{{{\text{Perimeter of Delta BDC}}}} \cr & = \frac{{6 + 7 + 8}}{{9 + 6 + 12}} \cr & = \frac{{21}}{{27}} \cr & = \frac{7}{9} \cr} $$Join The Discussion
Comments ( 4 )
Related Questions on Triangles
If ABC and PQR are similar triangles in which ∠A = 47° and ∠Q = 83°, then ∠C is:
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B. 70°
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In the following figure which of the following statements is true?
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Small c and refers to which angles.. the question is confusing.and the solution is more confusing.
what find in this quest
The question is not clear. What are we supposed to find here?
You have not given what to find