Determine the ratios - frac AD AB - frac DE BC A- 3 - 5-5 - 3B- 7 - 4-7 - 4C- 4 - 7-4 - 7D- 3 - 7-4 - 7

The correct option is C 4/7,4/7 We have AD/DB=4/3 ⇒DB/AD=3/4⇒AB AD/AD=3/4 AB/AD 1=3/4 AB/AD=3/4+1 ⇒AB/AD= 7/4⇒AD/AB=4/7 Since DE ∥ BC ∴∠ ADE = ∠ ABC [Corres ...

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Standard X

Mathematics

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Determine the...

Question

$I n f i g u r e, A B C i s a t r i a n g l e . D E i s p a r a l l e l t o B C a n d \frac{A D}{D B} = \frac{4}{3} D e t e r m i n e t h e r a t i o s \frac{A D}{A B}, \frac{D E}{B C}$

3/5, 5/3

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3/7, 4/7

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7/4, 7/4

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4/7,4/7

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Solution

The correct option is D
4/7,4/7

$W e h a v e \frac{A D}{D B} = \frac{4}{3} \Rightarrow \frac{D B}{A D} = \frac{3}{4} \Rightarrow \frac{A B - A D}{A D} = \frac{3}{4} \frac{A B}{A D} - 1 = \frac{3}{4} \frac{A B}{A D} = \frac{3}{4} + 1 \Rightarrow \frac{A B}{A D} = \frac{7}{4} \Rightarrow \frac{A D}{A B} = \frac{4}{7} S i n c e D E ∥ B C ∴ ∠ A D E = ∠ A B C [C o r r e s p o n d i n g a n g l e s] A n d, ∠ A E D = ∠ A C B [C o r r e s p o n d i n g a n g l e s] S o, b y A A - a x i o m o f s i m i l a r i t y, w e h a v e △ A D E \sim△ A B C \Rightarrow \frac{A D}{A B} = \frac{D E}{B C} [∵ C o r r e s p o n d i n g s i d e s o f s i m i l a r t r i a n g l e s a r e p r o p o r t i o n a l] \Rightarrow \frac{4}{7} = \frac{D E}{B C} \frac{D E}{B C} = \frac{4}{7}$

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In figure, ABC is a triangle .DE is parallel to BC and ADDB=43Determine the ratios ADAB,DEBC

$I n f i g u r e, A B C i s a t r i a n g l e . D E i s p a r a l l e l t o B C a n d \frac{A D}{D B} = \frac{4}{3} D e t e r m i n e t h e r a t i o s \frac{A D}{A B}, \frac{D E}{B C}$