Question

in triangle PQR, X, Y and Z are the midpoints of PQ, QR and RP respectively. If PQ=7.2 cm, PR=8.4cm and XZ=3.8 cm, then find the perimeter of triangle ABC

Answer 1

Given : ΔPQR, X, Y and Z are the midpoints of PQ, QR and RP respectively.  PQ=7.2 cm, PR=8.4cm and XZ=3.8 cm,

To  find  : the perimeter of ΔPQR  &  ΔXYZ

Solution:

line joining the mid-point of two sides of a triangle is equal to half the length of the third side

XZ = QR/2  

=> 3.8 = QR/2

=> QR = 7.6 cm

YZ = PQ/2

=> YZ = 7.2/2

=> YZ = 3.6 cm

XY = PR/2

=>XY = 8.4/2

=> XY = 4.2 cm

perimeter of ΔPQR = PQ + QR + PR

= 7.2 + 7.6 + 8.4

=  23.2 cm

perimeter of ΔXYZ = XY + YZ + XZ

=4.2 + 3.6 + 3.8

= 11.6 cm

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Answer 2

Answer:

• Perimeter of △XYZ is 11.6cm and △PQR is 23.2cm.

Step-by-step explanation:

Given:

△ PQR

X,Y,Z are the midpoints of PQ,QR,RP.

PQ = 7.2cm, PR = 8.4cm, XZ = 3.8cm

To find:

Perimeter of △PQR, △XYZ

Solution:

• Since, the line joining the mid point of the two sides of a triangle is equal to the half the length of the third side of the triangle.

⇒ XZ = QR/2

• 3.8 = QR/2
• QR = 7.6 cm

⇒ XY = PR/2

• XY = 8.4/2
• XY = 4.2 cm

⇒ YZ = PQ/2

• YZ = 7.2/2
• YZ = 3.6 cm

Now, perimeter of △XYZ

• XY + YZ + ZX
• 4.2 + 3.6 + 3.8
• 11.6 cm

Now, perimeter of △PQR

• PQ + QR + RP
• 7.2 + 7.6 + 8.4
• 23.2 cm

∴ The perimeters of △XYZ and △PQR are 11.6 cm and 23.2 cm respectively.