If O, P, equals, 26OP=26, P, N, equals, 20PN=20, O, N, equals, 30ON=30, S, Q, equals, 36SQ=36, and R, Q, equal

Question

If O, P, equals, 26OP=26, P, N, equals, 20PN=20, O, N, equals, 30ON=30, S, Q, equals, 36SQ=36, and R, Q, equals, 54RQ=54, find the perimeter of triangle, Q, R, S△QRS. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

GPT-5 mini · Answer

Note that RQ/ON = 54/30 = 1.8 and SQ/PN = 36/20 = 1.8, so triangle QRS is similar to triangle NOP with scale factor 1.8. Thus
RS = 1.8·OP = 1.8·26 = 46.8.

Perimeter = RQ + QS + RS = 54 + 36 + 46.8 = 136.8.

Answer: 136.8

If O, P, equals, 26OP=26, P, N, equals, 20PN=20, O, N, equals, 30ON=30, S, Q, equals, 36SQ=36, and R, Q, equals, 54RQ=54, find the perimeter of triangle, Q, R, S△QRS. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

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