Delta PNOcong Delta MNL What is the length of overline (OP) 10 meters 11 meters 38 meters 42 meters meters

To solve this problem, we need to use the information given about the congruent triangles \(\triangle PNO\) and \(\triangle MNL\).Given:- \(ON = (4x - 2)\) meters- \(PL = 38\) meters- \(KL = (3x + 5)\) meters- \(OM = 35\) meters- \(ML = 38\) meters- \(\triangle PNO \cong \triangle MNL\)Since \(\triangle PNO\) is congruent to \(\triangle MNL\), corresponding sides of the triangles are equal in length.Step 1: Set the lengths of the corresponding sides equal to each other.\(ON = KL\)\((4x - 2) = (3x + 5)\)Step 2: Solve for \(x\).\(4x - 2 = 3x + 5\)\(4x - 3x = 5 + 2\)\(x = 7\)Step 3: Now that we have the value of \(x\), we can find the length of \(OP\) by using the fact that \(OP = OM + ML\) because \(OP\) is the sum of the lengths of \(OM\) and \(ML\).\(OP = OM + ML\)\(OP = 35 + 38\)\(OP = 73\)However, none of the answer choices match 73 meters. Let's re-evaluate the information given and the congruence of the triangles.Since \(\triangle PNO\) is congruent to \(\triangle MNL\), and we are given that \(OM = 35\) meters and \(ML = 38\) meters, we can infer that \(OP = ML\) because they are corresponding sides of the congruent triangles.Therefore, the length of \(\overline{OP}\) is equal to the length of \(\overline{ML}\), which is given as 38 meters.Final Answer: The length of \(\overline{OP}\) is 38 meters.