Answer:
17 ft
Explanation:
You want the perimeter of ∆PQR shown as congruent to ∆STU. Sides are marked as PQ=ST=4 ft, QR=TU=6 ft, PR=(3y -2) ft, and SU=(y+4) ft.
Corresponding sides
Corresponding sides of congruent triangles are congruent. This means ...
PR = SU
3y -2 = y +4
2y = 6 . . . . . . . . add 2-y
y = 3
Then PR = (3·3 -2) ft = 7 ft.
Perimeter
The perimeter is the sum of the side lengths:
4 ft + 7 ft + 6 ft = 17 ft
The perimeter of triangle PQR is 17 feet.
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Additional comment
You know the triangles are congruent because corresponding sides have the same length (4 ft, 6 ft) and the angle between them is marked as the same in the two triangles. This is sufficient to claim SAS congruence.
One triangle, by itself, does not have enough information to tell us the value of y. So, we need to find a relationship between the two triangles. Ordinarily, we would expect the problem statement to tell us the triangles are similar or congruent, but it does not. That is why we examine the side lengths closely, and realize they are the same, with the angle marked as being the same.
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