What is the perimeter of triangle PQR? Show your work.

Answer:The perimeter of triangle PQR is 17 ftStep-by-step explanation:Consider the triangles PQR and STU1. PQ ≅ ST = 4 ft (Given)2. ∠PQR ≅ ∠STU  (Given)3. QR ≅ TU = 6 ft (Given)Therefore, the two triangles are congruent by SAS postulate.Now, from CPCTE, PR = SU. Therefore,[tex]3y-2=y+4\\3y-y=4+2\\2y=6\\y=\frac{6}{2}=3[/tex]Now, side PR is given by plugging in 3 for 'y'.PR = 3(3) - 2 = 9 - 2 = 7 ftNow, perimeter of a triangle PQR is the sum of all of its sides.Therefore, Perimeter = PQ + QR + PR                                    = (4 + 6 + 7) ft                                    = 17 ftHence, the perimeter of triangle PQR is 17 ft.