Question

9. In ∆PQR, X, Y and Z are the midpoints of
PQ, QR and RP respectively. If PQ = 7.2 cm,
PR = 8.4 cm and XZ = 3.8 cm, then find the
perimeter of ∆PQR and ∆XYZ.​

Answer 1

Answer:

Given:PQ=7.2cm

PR=8.4cm

XZ=3.8cm

so,

2XZ=QR (mid points of two sides of a triangle joint together are parallel and half of third side). -1 theorm

2x3.8=7.6cm

QR=7.6cm.

perimeter of a triangle=sum of all sides

p.of tri.PQR=PQ+QR+QP

=7.2+7.6+8.4

perimeter of triangle PQR =23.2cm

Now,XY=1/2PR. and ZX=1/2 PQ

(by 1st theorm mentioned above)

XY=1/2x8.4

=4.2cm

ZX=1/2x7.2

=3.6cm

perimeter of triangle XYZ=sum of sides

p. of triangle XYZ=XY+YZ+ZX

=3.6+4.2+3.8

perimeter of triangle XYZ=11.6cm