Question

BD is angle bisector of ∆ABC ,AD=X DC =X+2 , AB=X-2 , BC=X-1 , find the value of x ?
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Answer 1

Gɪᴠᴇɴ :-

• BD is angle bisector of ∆ABC .
• AD=X
• DC =X+2
• AB=X - 2
• BC=X - 1

Tᴏ Fɪɴᴅ :-

• value of x ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• The Angle-Bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides. (Refer To image .)

Sᴏʟᴜᴛɪᴏɴ :-

By Angle - Bisector Theoram we can say That :-

➪ AB/BC = AD/DC

Putting values Now, we get :-

➪ (x - 2)/(x - 1) = x/(x + 2)

cross - Multiply,

➪ (x - 2)(x + 2) = x(x - 1)

➪ x² - 4 = x² - x

➪ x = 4 (Ans.)

Hence, Value of x will be 4.

Answer 2

QUESTION :-

=> BD is angle bisector of ∆ABC ,AD=X DC =X+2 , AB=X-2 , BC=X-1 , find the value of x

Given :-

●BD is angle bisector of ∆ABC.

●AD = x.

●DC = x + 2.

●AB = x- 2.

●BC = x - 1.

To Find :-

■ Value of x.

Solution :-

=> According to angle - bisector theorem,

=> AB/BC = AD/DC

[ Now, putting values]

=>(x - 2)/(x - 1) = x/(x + 2)

[Now , apply cross multiplication.]

=>(x - 2)(x + 2) = x (x - 1)

=>x² - 4 = x² - x

=> - 4 = - x

=> .°. x = 4.

Therefore, the value of x is 4.