Question

P, Q, R are midpoint of sides of triangle ABC respectively find the ratio of perimeter of triangle PQR and triangle ABC....... need it urgently

Answer 1

Heya,
Here is ur answer hope it will help u

We know that mid point of line are half of lenght of the line

So midpoint PQ=AB/2

QR=BC/2
RP= CA/2


Now perimeter of triangle ABC = Ab+BC+CA


HENCE PERI.RTER of triangle pqr = AB+BC+CA/ 2


HENCE ratio is 1/2 ans....

Answer 2

Given:

P, Q, R are midpoints of sides of triangle ABC respectively.

To find:

The ratio of perimeter of ΔPQR and ΔABC

Solution:

Perimeter of ΔABC = AB + BC + AC

By midpoint theorem:

The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.

 $P Q=\frac{1}{2} B C$

 $Q R=\frac{1}{2} A B$

 $P R=\frac{1}{2} A C$

Perimeter of PQR:

             $=\frac{1}{2} B C+\frac{1}{2} A B+\frac{1}{2} A C$

             $=\frac{1}{2}(B C+A B+A C)$

$\frac{\text { Perimeter of } \Delta P Q R}{\text { Perimeter of } \triangle A B C}=\frac{\frac{1}{2}(A B+B C+A C)}{A B+B C+A C}$

Cancel the common terms, we get

$\frac{\text { Perimeter of } \Delta P Q R}{\text { Perimeter of } \Delta A B C}=\frac{1}{2}$

The ratio of perimeter of ΔPQR and ΔABC is  $\frac{1}{2}$.

To learn more...

1. P,Q,R are the midpoints of sides of triangle ABC respectively.Find the ratio of perimeters of triangle PQR and triangle ABC.

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2. 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

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