Question

solve for side or perimeter, similar triangles
question
find the perimeter of △wxy. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

Explanation:

Step1: Confirm similarity by AA

△TVU and △YXW have angles 41°, 58°, 81° (AA similarity).

Step2: Identify corresponding sides

Corresponding sides: TV↔YW, TU↔XW, VU↔XY.

Step3: Calculate scale factor

Scale factor k = YW/TV = 36/103 ≈ 0.3495.

Step4: Find unknown side XY

XY = VU×k = 68×(36/103) ≈ 23.77.

Step5: Compute perimeter

Perimeter = YW + XW + XY ≈ 36 + 31.2 + 23.77 ≈ 90.97.

Step6: Round to nearest tenth

90.97 ≈ 91.0.

Answer:

91.0