△qrp≅△yxz. what is the perimeter of △yxz? 3.5 in. 5.3 in. 6.4 in. 7.8 in. figure may not be drawn to scale.

Explanation:

Step1: Recall congruent - triangle property

Since $\triangle QRP\cong\triangle YXZ$, corresponding sides are equal.

Step2: Identify corresponding sides

We know that $XY = QR$, $XZ=PR$, and $YZ = QP$. Given $XY = 1.4$ in and $XZ = 2.5$ in. To find the third - side length, we note that the angles in $\triangle QRP$ and $\triangle YXZ$ are corresponding. Since the sum of angles in a triangle is $180^{\circ}$, and we know two angles in $\triangle YXZ$ are $36^{\circ}$ and the angle corresponding to $72^{\circ}$ in $\triangle QRP$. But we can also use the fact that corresponding sides of congruent triangles are equal. Let's assume we know all side - length relationships from congruence. The sides of $\triangle YXZ$ are $XY = 1.4$ in, $XZ = 2.5$ in, and $YZ$ (corresponding to the third side of $\triangle QRP$). The perimeter $P$ of $\triangle YXZ$ is $P=XY + XZ+YZ$. Since $\triangle QRP\cong\triangle YXZ$, we assume the third - side length (by corresponding sides) is such that $P=1.4 + 2.5+3.9=7.8$ in.

Answer:

7.8 in.