Question

△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: Find the third angle of \(\triangle QRP\)

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle of \(\triangle QRP\) be \(\angle R\).
\(\angle R=180^{\circ}-(72^{\circ} + 36^{\circ})=72^{\circ}\)
Since \(\triangle QRP\cong\triangle YXZ\), corresponding sides are equal. \(YZ = RP = 2.5\) in, \(XZ=QR\), \(XY = 1.4\) in.

Step2: Calculate the perimeter of \(\triangle YXZ\)

Perimeter \(P=XY + YZ+XZ\).
Since \(\triangle QRP\cong\triangle YXZ\), \(XZ = QR\), \(XY = 1.4\) in, \(YZ = 2.5\) in.
\(P=1.4 + 2.5+3.9\) (By angle - side relationship in \(\triangle QRP\) (isosceles as two angles \(72^{\circ}\)), \(QR = RP = 3.9\) in, and \(XZ=QR\))
\(P = 7.8\) in

Answer:

\(7.8\) in.