Question

ps is the bisector of angle p of triangle pqr. pq= 4cm , pr=2(x-1) , QS= X , SR = X+2

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given: A triangle PQR in which PS is the internal bisector of angle P.

To find:X

First we have to prove,

QS/SR=PQ/PR

Construction: Draw RE parallel PS to meet QP produced in E.

Proof:

Here we have,

ER || PS

Then,

angle 2 = angle 3.........1 (alternative angles)

and,

angle 1 = angle 4....... 2 (corresponding angles)

Given that PS in an angular bisector

then,we have

angle 1 = angle 2........3

By eq1 , eq2 , eq3 we get,

angle 3 = angle 4

Then,

PR=PE...........4 (sides opposite to equal angles)

In triangle QRE we have,

RE || PS

By basic proportionality theorem we get,

QS/SR = QP/PE

QS/SR = QP/PR

QS/SR = PQ/PR

Now, Putting values of QS, SR, QP, PR

X/X+2=4/2X-2

By cross multiplication

2X²-2X=4X+8

2X²-6X-8=0

Dividing by 2 for simplifying

X²-3X-4=0

By factorisation

X²-4X+1X-4=0

X(X-4)+1(X-4)=0

(X+1) (X-4)=0

Therefore, X=-1 or X=+4

Length cannot be negative

Therefore, X=4

PR=7

QS=4

SR=6

Hope it's helpful to you

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