Answer: 6.4 inches
Step-by-step explanation:
As given triangle QRP is congruent to triangle YXZ.
where ∠Q=72°
PR =2.5 inches
∠Z=36°
XY=1.4 inches.
then QP=YZ,PR=YZ=2.5 , QR=XY=1.4 inches,∠Q=∠Y=72°,
∠P=∠Z=36° and ∠R=∠X= 180°-36°-72°=72°(by angle sum property)
As ∠Y=∠X=72° Hence triangle XYZ is a isosceles triangle .
We know that "Sides opposite to equal angles of a triangle are equal"
⇒YZ=XZ=2.5 inches
Thus the perimeter of triangle YXZ=YX+XZ+ZY=1.4+2.5+2.5=6.4 inches.
