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Converse of BPT

In Δ ABC, DE ...

Question

$I n Δ A B C, D E | | B C a n d \frac{A D}{D B} = \frac{3}{5} .$ If $A C = 5.6 c m$ , then $A E =$ _____.

A

2.1 cm

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B

2.4 cm

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C

3.2 cm

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D

3.6 cm

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Solution

The correct option is A
2.1 cm

$I n Δ A B C, D E | | B C (G i v e n) \frac{A D}{A B} = \frac{A E}{A C} [B a s i c P r o p o r t i o n a l i t y T h e o r e m]$
$∵ A B = (3 + 5), A D = 3 A C = 5.6 c m (G i v e n)$

$\frac{3}{3 + 5} = \frac{A E}{5.6}$

$\frac{3}{8} = \frac{A E}{5.6}$

$A E = \frac{3 \times 5.6}{8} = 3 \times 0.7 = 2.1 c m$

$\Rightarrow A E = 2.1 c m$

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Δ A B C, D E / / B C

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