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Converse of Basic Proportionality Theorem

ABC is a tria...

Question

$A B C$ is a triangle and $D E$ is drawn parallel to $B C$ cutting the other sides at $D$ and $E$ . If $A B = 3.6 c m$ , $A C = 2.4 c m$ and $A D = 2.1 c m$ , then $A E$ is equal to:

1.4 c m

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1.8 c m

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1.2 c m

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1.05 c m

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Solution

The correct option is A $1.4 c m$
Given: $△ A B C$ , $D E ∥ B C$
In $△ A B C$ and $△ D E A$ ,
$∠ B A C = ∠ D A E$ ...(Common angles)
$∠ A B C = ∠ A D E$ ...(Corresponding angles)
$∠ A C B = ∠ A E D$ ...(Corresponding angles)
Thus, $△ A B C \sim △ A D E$ ...( $A A A$ rule)
Hence, $\frac{A B}{A D} = \frac{A C}{A E}$ ...(Corresponding sides)

$∴ \frac{3.6}{2.1} = \frac{2.4}{A E}$

$A E = \frac{2.1 \times 2.4}{3.6}$
$A E = 1.4$ cm

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Similar questions

ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm, then AE equal to -

In triangle ABC, points D and E lie on sides AB and AC respectively such that DE is parallel to BC.

If AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm, then AE is equal to ____.

A B C

is a triangle and

D E

is drawn parallel to

B C

cutting the other sides at

D

and

E

. If

A B = 3.6 c m, A C = 2.4 c m

and

A D = 2.1 c m

, then

A E

= ______.

D

and

E

are points on the sides

A B

and

A C

respectively of

△ A B C

. For the following case, state whether

D E ∥ B C

A B = 5.6 c m, A D = 1.4 c m, A C = 9.6 c m

and

E C = 2.4 c m

Q. In given figure

D

and

E

are respectively the points on the sides

A B

and

A C

of a

△ A B C

such that

A B = 5.6 c m, A D = 1.4 c m, A C = 7.2 c m

and

A E = 1.8 c m

. Then show that

D E | | B C

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ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB=3.6 cm, AC=2.4 cm and AD=2.1 cm, then AE is equal to:

The correct option is A 1.4 cmGiven: △ABC, DE∥BCIn △ABC and △DEA,∠BAC=∠DAE ...(Common angles)∠ABC=∠ADE ...(Corresponding angles)∠ACB=∠AED ...(Corresponding angles)Thus, △ABC∼△ADE ...(AAA rule)Hence, ABAD=ACAE ...(Corresponding sides)∴3.62.1=2.4AEAE=2.1×2.43.6AE=1.4 cm

$A B C$ is a triangle and $D E$ is drawn parallel to $B C$ cutting the other sides at $D$ and $E$ . If $A B = 3.6 c m$ , $A C = 2.4 c m$ and $A D = 2.1 c m$ , then $A E$ is equal to: