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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to Be Parallel

In a Δ ABC,...

Question

In a $Δ A B C$ , $D$ and $E$ are points on the sides $A B$ and $A C$ respectively such that $D E | | B C$ .
If $A D = 6 c m, D B = 9 c m$ and $A E = 8 c m$ , find $A C$ .

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Solution

$\begin{matrix} D E ∥ B C ∴ \frac{A D}{A B} = \frac{A E}{E C} \frac{6}{9} = \frac{8}{E C} E C = 12 A C = A E + E C = 8 + 12 = 20 o r \frac{A D}{A B} = \frac{A E}{E C} \frac{6}{15} = \frac{8}{A C} 4 \times 5 = A C o r A C = 20 c m \end{matrix}$

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Similar questions

Q. In a

Δ 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 c m, A B = 6 c m

and

A C = 9 c m

, find

A E

Q. In a

Δ A B C

D

and

E

are points on the sides

A B

and

A C

respectively such that

D E | | B C

.
If

\frac{A D}{D B} = \frac{2}{3}

and

A C = 18 c m

, find

A E

D and E are the points on the sides AB and AC respectively of a $Δ A B C$ such that: AD = 8 cm, DB =12 cm, AE = 6cm and CE = 9 cm. Prove that $B C = \frac{5}{2} D E$ .

Q. In a

Δ 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 = 8 c m, A B = 12

and

A E = 12 c m

, find

C E

State true or false:

Δ A B C

, D and E are the points on sides AB and AC respectively. If

A B = 9 c m, A D = 4 c m, A E = 6 c m

and

E C = 7.5 c m

, then

D E ∥ B C

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In a ΔABC, D and E are points on the sides AB and AC respectively such that DE||BC.If AD=6 cm,DB=9 cm and AE=8 cm, find AC.

DE∥BC∴ADAB=AEEC69=8ECEC=12AC=AE+EC=8+12=20orADAB=AEEC615=8AC4×5=ACorAC=20cm

In a $Δ A B C$ , $D$ and $E$ are points on the sides $A B$ and $A C$ respectively such that $D E | | B C$ .
If $A D = 6 c m, D B = 9 c m$ and $A E = 8 c m$ , find $A C$ .

$\begin{matrix} D E ∥ B C ∴ \frac{A D}{A B} = \frac{A E}{E C} \frac{6}{9} = \frac{8}{E C} E C = 12 A C = A E + E C = 8 + 12 = 20 o r \frac{A D}{A B} = \frac{A E}{E C} \frac{6}{15} = \frac{8}{A C} 4 \times 5 = A C o r A C = 20 c m \end{matrix}$