In - ABC - AC -15 cm and DE BC- If AB - AD -3- find EC-A- 5 cmB- 10 cmC- 2-5 cmD- 9 cm

The correct option is B 10 cm From basic proportionality theorem, since, DE ∥ BC, AD/DB=AE/EC AB/AD=AD+DB/AD=1+DB/AD ⇒ 1+DB/AD=3 ⇒DB/AD=2 ⇒AD/DB=AE/EC=1/2 ⇒ ...

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Byju's Answer

Standard X

Mathematics

Converse of BPT

In Δ ABC , AC...

Question

In $Δ A B C, A C = 15 c m$ and $D E ∥ B C$ . If $\frac{A B}{A D} = 3$ , find EC.

$5 c m$

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$10 c m$

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$2.5 c m$

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$9 c m$

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Solution

The correct option is B
$10 c m$

From basic proportionality theorem, since, $D E ∥ B C$ ,
$\frac{A D}{D B} = \frac{A E}{E C}$
$\frac{A B}{A D} = \frac{A D + D B}{A D} = 1 + \frac{D B}{A D} \Rightarrow 1 + \frac{D B}{A D} = 3 \Rightarrow \frac{D B}{A D} = 2 \Rightarrow \frac{A D}{D B} = \frac{A E}{E C} = \frac{1}{2} \Rightarrow 2 A E = E C \Rightarrow A C = A E + E C$ -------(1)
Substituting value of EC and AC in (1),
$\Rightarrow 15 = 3 A E \Rightarrow 5 = A E \Rightarrow E C = 10 c m$

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In ΔABC, AC=15 cm and DE∥BC. If ABAD=3, find EC.

The correct option is B 10 cm From basic proportionality theorem, since, DE∥BC, ADDB=AEEC ABAD=AD+DBAD=1+DBAD⇒1+DBAD=3⇒DBAD=2⇒ADDB=AEEC=12⇒2AE=EC⇒AC=AE+EC -------(1) Substituting value of EC and AC in (1), ⇒15=3AE⇒5=AE⇒EC=10 cm

In $Δ A B C, A C = 15 c m$ and $D E ∥ B C$ . If $\frac{A B}{A D} = 3$ , find EC.