The perimeter of triangle FGH is 50 units, as determined by the midsegment property, where each midsegment is parallel to a corresponding side and half its length. Here option A is correct.
The diagram shows triangle FGH with midsegments IJ, JK, and IK. We are asked to find the perimeter of triangle FGH.
Midsegment Property: A midsegment in a triangle is parallel to a third side of the triangle and half its length.
Identify Midsegments and Sides:
Segment IJ is parallel to side FG and half its length. Therefore, IJ = FG/2.
Segment JK is parallel to side GH and half its length. Therefore, JK = GH/2.
Segment IK is parallel to side FH and half its length. Therefore, IK = FH/2.
Perimeter Calculation:
The perimeter of a triangle is the sum of the lengths of its sides.
Perimeter of triangle FGH = FG + GH + FH
Substitute the midsegment lengths from step 2: Perimeter = 2IJ + 2JK + 2*IK Perimeter = 2(FG/2) + 2(GH/2) + 2(FH/2) Perimeter = FG + GH + FH
Perimeter is Given:
The problem states that the perimeter of triangle FGH is 50 units.
Therefore, FG + GH + FH = 50 units. Here option A is correct.