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

Byju's Answer

Standard VII

Mathematics

Construction of an Isosceles Triangle Triangle

In fig., AD i...

Question

In fig., AD is the bisector of $∠$ BAC. If AB =10 cm. AC =14 cm and BC = 6 cm, find BD and DC.

Open in App

Solution

Let BD = $x$ cm. Then, DC = (6 - $x$ ) cm.

Since AD is the bisector of $∠$ A.

$∴$ $\frac{A B}{A C}$ = $\frac{B D}{D C}$

$\Rightarrow$ $\frac{10}{14}$ = $\frac{x}{6 - x}$

$\Rightarrow$ $\frac{5}{7}$ = $\frac{x}{6 - x}$

$\Rightarrow$ 30 - 5 $x$ = 7 $x$ [ $∵$ AC = 5.6]

$\Rightarrow$ 12 $x$ = 30

$\Rightarrow$ $x$ = $\frac{5}{2}$ = 2.5 cm

$\Rightarrow$ BD = 2.5 cm and DC = (6 - $x$ ) cm

= (6 - 2.5) cm = 3.5 cm

Suggest Corrections

Similar questions

In a $Δ A B C$ , AD is the bisector of $∠ A$ .

(i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.

(ii) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

(iii) If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC.

(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

Q. In

Δ A B C

A D

is the bisector of

∠ B A C

. If

A B = 10 c m, A C = 14 c m

and

B C = 6 c m

, then

B D

is:

Q. In the figure given below

A D

is bisector of

∠ B A C

. If

A B = 6 c m, A C = 4 c m

and

B D = 3 c m

, find

B C

Q. In a

Δ A B C, A D

is the bisector of

∠ A,

meeting side

B C

D

.
If

A B = 10 c m

A C = 14 c m

and

B C = 6 c m

,
Find

B D

and

D C

In a $Δ A B C$ , AD is the bisector of $∠ A$ , meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
(viii) If AB =10 cm, AC = 6 cm and BC = 12 cm, find BD and DC

Join BYJU'S Learning Program

In fig., AD is the bisector of ∠BAC. If AB =10 cm. AC =14 cm and BC = 6 cm, find BD and DC.

Let BD = xcm. Then, DC = (6 - x) cm. Since AD is the bisector of ∠A. ∴ ABAC = BDDC ⇒ 1014 = x6−x ⇒ 57 = x6−x ⇒ 30 - 5x = 7x [∵ AC = 5.6] ⇒ 12x = 30 ⇒ x = 52 = 2.5 cm ⇒ BD = 2.5 cm and DC = (6 - x) cm = (6 - 2.5) cm = 3.5 cm

In fig., AD is the bisector of $∠$ BAC. If AB =10 cm. AC =14 cm and BC = 6 cm, find BD and DC.