Answer:
46.8
Step-by-step explanation:
The missing angle in ∆PQR is 180° -76° -41° = 63°. Two angles are the same between the triangles, so we know they are similar. Side lengths of similar triangles are proportional.
Corresponding sides of the triangles are ...
ST ⇔ PQ ratio ST/PQ = 16.8/14 = 1.2
TU ⇔ QR ratio TU/QR = x/10 = 1.2 ⇔ x = 12
US ⇔ RP ratio US/RP = 18/15 = 1.2
The perimeter of ∆STU is the sum of its side lengths ...
16.8 +12 +18 = 46.8 . . . units
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Additional comment
The perimeter of PQR is 14 +10 +15 = 39. The scale factor applies to the perimeter, just as it does to the side lengths.
The perimeter of STU is 1.2×39 = 46.8.
