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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 $A E$ = ______.

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 $1.4 c m$
By Basic Proportionality Theorem,
$\frac{B D}{A D} = \frac{C E}{A E}$
$\frac{B D}{A D} + 1 = \frac{C E}{A E} + 1$
$\frac{A D + B D}{A D} = \frac{A E + C E}{A E}$
$\frac{A B}{A D} = \frac{A C}{A E}$
Subtituting values:
$\frac{3.6}{2.1} = \frac{2.4}{A E}$
$A E = \frac{2.1 \times 2.4}{3.6} = 1.4 c m$

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Similar questions

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:

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

= ______.

Q. In a

△ A B C, D

and

E

are points on the sides

A B

and

A C

respectively such that

D E ∥ B C

. If

A D = 2.4 c m, A E = 3.2 c m, D E ∥ B C

. If

A D = 2.4 c m, A E = 3.2 c m, D E = 2 c m

and

B C = 5 c m

, find

B D

and

C E

Q. Assertion :If in a

△ A B C

, a line

D E ∥ B C

, intersects AB in D and AC in E, then

\frac{A B}{A D} = \frac{A C}{A E}

. Reason: If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.

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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 = ______.

The correct option is A 1.4 cmBy Basic Proportionality Theorem, BDAD=CEAE BDAD+1=CEAE+1 AD+BDAD=AE+CEAE ABAD=ACAE Subtituting values: 3.62.1=2.4AE AE=2.1×2.43.6=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 $A E$ = ______.