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Consider the triangle shown in the figure where BC = 12 cm, Db = 9 cm, CD = 6 cm and 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
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Consider the triangle shown in the figure where BC = 12 cm, Db = 9 cm,...
Here, ∠ACB = c+180-(2c-b) = 180-(b+c)
So, We can say that Δ BCD and &delta ABC will be similar.
According to property of similarity,
AB/12 = 12/9
Hence,
AB = 16
AC/6 = 12/9
AC = 8
Hence, AD = 7 and AC = 8
Now,
Perimeter of Delta; ADC / Perimeter of &delta BDC,
= (6+7+8)/(9+6+12)
= 21/27 = 7/9.
So, We can say that Δ BCD and &delta ABC will be similar.
According to property of similarity,
AB/12 = 12/9
Hence,
AB = 16
AC/6 = 12/9
AC = 8
Hence, AD = 7 and AC = 8
Now,
Perimeter of Delta; ADC / Perimeter of &delta BDC,
= (6+7+8)/(9+6+12)
= 21/27 = 7/9.
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Consider the triangle shown in the figure where BC = 12 cm, Db = 9 cm,...
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Consider the triangle shown in the figure where BC = 12 cm, Db = 9 cm, CD = 6 cm andWhat is the ratio of the perimeter of the triangle ADC to that of the triangle BDC ?a)7:9b)8:9c)6:9d)5:9e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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