Question

In triangle a b c the lines are drawn parallel to bc,ca,ab respectively through a,b,c intersecting at p,q,r find the ratio of perimeter of triangle p,q,r and triangle a,b,c

Answer 1

Given:
AB || PR, BC || QR, AC || PQ
To Find:
Perimeter of triangle PQR : Perimeter of triangle ABC.
Solution:
AC || PQ (Given)
AC || BQ
Similarly, BC || AQ
Therefore, AQBC is a parallelogram.
Similarly, ARCB & ABPC are parallelograms.
AQ = BC___1
AR = BC___2
(opposite sides of parallelogram are equal)
Adding equations 1 and 2,
BC + BC = AQ + AR
2BC = QR
Similarly, 2AB = PR
2AC = PQ
Perimeter of triangle ABC
= AB + BC + AC
Perimeter of triangle PQR
= PQ + QR + PR
= 2AC + 2BC + 2AB
= 2(AB + BC + AC)
Ratio of perimeters of triangle PQR & triangle ABC
$= \frac{perimeter \: of \: triangle \: pqr}{perimeter \: of \: triangle \: abc}$
$= \frac{2(ab + bc + ac)}{(ab + bc + ca)}$
$= \frac{2}{1}$
Ratio of perimeters = 2:1

If it helped you, please press the 'Thank You' button and mark the answer as the Brainliest. Please!

Answer 2

Given:

AB || PR, BC || QR, AC || PQ

To Find:

Perimeter of triangle PQR : Perimeter of triangle ABC.

Solution:

AC || PQ (Given)

AC || BQ

Similarly, BC || AQ

Therefore, AQBC is a parallelogram.

Similarly, ARCB & ABPC are parallelograms.

AQ = BC___1

AR = BC___2

(opposite sides of parallelogram are equal)

Adding equations 1 and 2,

BC + BC = AQ + AR

2BC = QR

Similarly, 2AB = PR

2AC = PQ

Perimeter of triangle ABC

= AB + BC + AC

Perimeter of triangle PQR

= PQ + QR + PR

= 2AC + 2BC + 2AB

= 2(AB + BC + AC)

Ratio of perimeters of triangle PQR & triangle ABC

Ratio of perimeters = 2:1

If it helped you, please press the 'Thank You' button and mark the answer as the Brainliest. Please!

Read more on Brainly.in - https://brainly.in/question/2606088#readmore