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Standard X

Mathematics

Basic Proportionality Theorem

In a Δ ABC,...

Question

In a $Δ A B C$ , $D$ is any point on $A B$ and $D E | | B C$ meets $A C$ at E if $A D = 2.5, D B = 6$ cm and $A E = 3$ cm, then $E C =$

9.5

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7.2

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6.5

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12.5

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Solution

The correct option is B $7.2$ cm
Given: In $△ A B C$
$D E ∥ B C$
Then, $\frac{A D}{D B} = \frac{A E}{E C}$ ...(Basic Proportionality theorem)
$\frac{2.5}{6} = \frac{3}{E C}$
$E C = \frac{18}{2.5}$ .
$E C = 7.2$ .

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Similar questions

Q. In

Δ A B C

, DE is || to BC, meeting AB and AC at D and E. If AD = 3 cm, DB = 2 cm and AE = 2.7 cm, then AC is equal to:

Q. D and E are points on the sides AB and AC respectively of a

∆ A B C

. In each of the following cases, determine whether

D E ∥ B C

or not.

(i)

A D = 5.7 cm, D B = 9.5 cm, B D = 4.8 cm and E C = 8 cm .

(ii)

A B = 11.7 cm, A C = 11.2 cm, B D = 6.5 cm and A E = 4.2 cm .

(iii)

A B = 10.8 cm, A D = 6.3 cm, A C = 9.6 cm and E C = 4 cm .

(iv)

A D = 7.2 cm, A E = 6.4 cm, A B = 12 cm and A C = 10 cm .

D and E are points on the sides AB and AC respectively of a $Δ A B C$ . In each of the follwing cases, determine whether DE || BC or not.

(i) AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm and EC = 8 cm.

(ii) AB = 11.7 cm, AC = 11.2 cm, BD = 6.5 cm and AE = 4.2 cm.

(iii) AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm and EC = 4 cm.

(iv) AD = 7.2 cm, AE = 6.4 cm, AB = 12 cm and AC = 10 cm.

Q. In

Δ A B C

D E ∥ B C

Find

A D

D B =

7.2

cm,

A E = 1.8

cm, and

E C = 5.4

cm.

In a $Δ A B C$ , D and E are points on the sides AB and AC respectively. For each of the following cases show that DE || BC:
(i) AB = 12cm, AD = 8 cm, AE = 12 cm and AC= 18cm.
(ii)AB = 5.6cm, AD= 1.4cm, AC = 7.2 cm and AE= 1.8 cm.
(iii) AB= 10.8 cm, BD= 4.5cm, AC = 4.8cm and AE =2.8 cm.
(iv)AD = 5.7cm, BD = 9.5cm, AE = 3.3cm and EC = 5.5 cm.

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In a ΔABC, D is any point on AB and DE||BC meets AC at E if AD=2.5,DB=6 cm and AE=3 cm, then EC=

The correct option is B 7.2 cmGiven: In △ABCDE∥BCThen, ADDB=AEEC ...(Basic Proportionality theorem)2.56=3EC EC=182.5.EC=7.2.

In a $Δ A B C$ , $D$ is any point on $A B$ and $D E | | B C$ meets $A C$ at E if $A D = 2.5, D B = 6$ cm and $A E = 3$ cm, then $E C =$

The correct option is B $7.2$ cm
Given: In $△ A B C$
$D E ∥ B C$
Then, $\frac{A D}{D B} = \frac{A E}{E C}$ ...(Basic Proportionality theorem)
$\frac{2.5}{6} = \frac{3}{E C}$
$E C = \frac{18}{2.5}$ .
$E C = 7.2$ .