You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Converse of BPT

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 $A D = x, D B = x - 2, A E = x + 2$ and $E C = x - 1$ , find the value of $x$ .

Open in App

Solution

$\begin{matrix} I n Δ A B C & Δ A D E ∠ A = ∠ A & ∠ A B C = ∠ A D E ∴ Δ A B C \sim Δ A D E [A A s i m i l a r i t y] \frac{A B}{A D} = \frac{A C}{A E} \frac{A B}{A D} - 1 = \frac{A C}{A E} - 1 \frac{A B - A D}{A D} = \frac{A C - A E}{A E} \Rightarrow \frac{D B}{A D} = \frac{E C}{A E} \Rightarrow \frac{x - 2}{x} = \frac{x - 1}{x + 2} (x - 2) (x + 2) = x (x - 1) x^{2} - 4 = x^{2} - x ∴ x = 4 \end{matrix}$

Suggest Corrections

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 = 4, A E = 8, D B = x - 4

, and

E C = 3 x - 19

, find

x

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 x - 7, D B = 5 x - 3, A E = 4 x - 3

and

E C = (3 x - 1)

, find the value of

x

D and E are points on the sides AB and AC respectively of a $Δ A B C$ such that DE || BC
Find the value of x, when

(i) AD = x cm, DB = (x - 2) cm,

AE = (x + 2) cm and EC = (x - 1) cm.

(ii) AD = 4 cm, DB = (x - 4) cm, AE = 8 cm and EC = (3x - 19) cm.

(iii) AD = (7x - 4) cm, AE = (5x - 2) cm, DB = (3x + 4 ) cm and EC = 3x cm.

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

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}{B D} = \frac{4}{5}

and

E C = 2.5 c m

, find

A E

Join BYJU'S Learning Program

In a ΔABC, D and E are points on the sides AB and AC respectively such that DE||BC.If AD=x,DB=x−2,AE=x+2 and EC=x−1, find the value of x.

InΔABC&ΔADE∠A=∠A&∠ABC=∠ADE∴ΔABC∼ΔADE[AAsimilarity]ABAD=ACAEABAD−1=ACAE−1AB−ADAD=AC−AEAE⇒DBAD=ECAE⇒x−2x=x−1x+2(x−2)(x+2)=x(x−1)x2−4=x2−x∴x=4

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 $A D = x, D B = x - 2, A E = x + 2$ and $E C = x - 1$ , find the value of $x$ .