Answer:
Yes. but under the next condition m∠Q ≅ m∠T
Explanation:
If the circular arc label of the angles ∠Q and ∠T means that they are congruent (equal) or m∠Q ≅ m∠T, in that case we can prove that ΔPQR is congruent with ΔSTU or ΔPQR≅ΔSTU.
We need three elements to form congruency statement.
1. Sides PQ ≅ ST = 4 ft
2. Angles m∠Q ≅ m∠T
2. Sides QR ≅ TU = 6 ft
Based on the SAS statement ( Side-Angle-Side) we prove that:
ΔPQR ≅ ΔSTU.
If they are congruent, every corresponding elements are congruent:
Sides PR = SU => 3y - 2 = y + 4 => 3y - y = 4 + 2 => 2y = 6 => y = 6/2 = 3
y = 3 => PR = 3 · 3 - 2 = 9 - 2 = 7 => PR = 7 ft
Perimeter of ΔPQR is
P = PQ + QR + PR = 4 + 6 + 7 = 17 ft
P = 17 ft
God with you!!!