Answer:
The perimeter of triangle PQR is 17 ft
Step-by-step explanation:
Consider the triangles PQR and STU
1. 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 ft
Now, perimeter of a triangle PQR is the sum of all of its sides.
Therefore, Perimeter = PQ + QR + PR
= (4 + 6 + 7) ft
= 17 ft
Hence, the perimeter of triangle PQR is 17 ft.
