If O, M, equals, 61OM=61, M, N, equals, 54MN=54, O, N, equals, 81ON=81, P, Q, equals, 27PQ=27, and R, Q, equals, 40, point, 5RQ=40.5, find the perimeter of triangle, P, Q, R△PQR.

Answer 1

To find the perimeter of triangle \( PQR \), we need to determine the lengths of the sides \( PQ \), \( QR \), and \( RP \).

From the problem statement, we have:

• \( 61OM = 61 \) implies that \( OM = 1 \)
• \( 54MN = 54 \) implies that \( MN = 1 \)
• \( 81ON = 81 \) implies that \( ON = 1 \)
• \( 27PQ = 27 \) implies that \( PQ = 1 \)
• \( 40.5RQ = 40.5 \) implies that \( RQ = 1 \)

Now, we can summarize the edges of triangle \( PQR \):

• \( PQ = 1 \)
• \( QR = 1 \)
• \( RP = 1 \)

The perimeter of triangle \( PQR \) is the sum of its side lengths:

\[ \text{Perimeter} = PQ + QR + RP = 1 + 1 + 1 = 3. \]

Thus, the perimeter of triangle \( PQR \) is \( \boxed{3} \).