Find the perimeter of △EFG. Round your answer to the nearest tenth if necessary. Figures are not necessarily d

Question

Find the perimeter of △EFG. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale. DCB numbers are 68, 60, and 84 with angles of 53, 45, and 82. EFG numbers are 42, 34, and x with angles of 45, 53, and 82. What is the x in EFG.

GPT-5 mini · Answer

Triangles EFG and DCB are similar (same angles). Match corresponding sides opposite equal angles: the side opposite 53° is 68 in DCB and 34 in EFG, so the scale factor is 34/68 = 1/2.

Thus x (side opposite 82°) = (1/2)·60 = 30.

Perimeter of △EFG = 42 + 34 + 30 = 106.

Find the perimeter of △EFG. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale. DCB numbers are 68, 60, and 84 with angles of 53, 45, and 82. EFG numbers are 42, 34, and x with angles of 45, 53, and 82. What is the x in EFG.

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