A line parallel to BC in $△$ ABC meets AB and AC in D and E respectively. If AD = (4x - 3)cm, DB = (3x - 1) cm, AE = (8x - 7)cm, EC = (5x -3)cm, the admissible value of x is

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $1$
$D E ∥ B C$
Thus, $\frac{A D}{D B} = \frac{A C}{E C}$
$\Rightarrow \frac{4 x - 3}{3 x - 6} = \frac{8 x - 7}{5 x - 3}$
$\Rightarrow 20 x^{2} - 27 x + 9 = 24 x^{2} - 29 x + 7$
$\Rightarrow 4 x^{2} - 2 x - 2 = 0$
$\Rightarrow 2 x^{2} - x - 1 = 0$
$\Rightarrow (2 x + 1) (x - 1) = 0$
Thus, $x = 1$

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 = 8 x - 7, D B = 5 x - 3, A E = 4 x - 3

and

E C = (3 x - 1)

, find the value of

x

In a \Delta ABC, D and E are points on the sides AB and AC respectively such that DE||BC.
(i) If AD = 6cm, DB = 9 cm and AE = 8 cm, find AC.
(ii) If $\frac{A D}{D B} = \frac{3}{4}$ and AC = 15 cm, find AE.
(iii) If $\frac{A D}{D B} = \frac{2}{3}$ and AC = 18 cm, find AE.
(iv) If AD = 4, AE=8, DB =x-4, and EC = 3x - 19 find x
(v) If AD = 8 cm, AB=12 cm and AE = 12 cm, finde CE.
(vi) If ad = 4 CM, db = 4.5 cm and AE = 8 cm, find AC
(vii) If AD = 2 cm, AB = 6 cm and AC = 9cm, find AE.
(viii) If $\frac{A D}{B D} = \frac{4}{5}$ and 3C = 2.5 cm, find AE.
(ix) If AC=x, DB=x-2, AE=x+2 and EC=x-1, find the value of x.
(x) If AD= 8x -7. DB= 5x-3, AE=4x-3 and EC= (3x-1), find the value of x.
(xi) If AD= 4x-3, AE=8x -7, BC=3x-1 and CE=5x-3, find the value x.
(xii) If AD=2.5 cm, BD= =3.0 cm and AE=3.75 cm, find the length of AC.