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 \(180^{\circ}\). In \(\triangle QRP\), if \(\angle Q = 72^{\circ}\) and assume the triangle is isosceles (since \(QP = RP\) as per the congruence and markings), then \(\angle R=36^{\circ}\) (because \(180-(72 + 72)=36\)). Since \(\triangle QRP\cong\triangle YXZ\), in \(\triangle YXZ\), \(YZ = RP=2.5\) in (corresponding parts of congruent triangles are equal), \(XY = 1.4\) in (given), and \(XZ=QR\).

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

The perimeter \(P\) of a triangle is \(P=a + b + c\). Here \(a = 1.4\), \(b = 2.5\), \(c = 3.9\) (since \(QR = XZ\), and using the side - angle - side congruence, \(QR = 3.9\) (by triangle properties and congruence). \(P=1.4+2.5 + 3.9=7.8\) in.

Answer:

\(7.8\) in.