Answer: Perimeter of triangle ROA = 33
=================================================
Explanation:
Points R, O, and A are midpoints of sides XY, YG, and XG respectively.
Because of this, we know that the points cut those sides into two equal halves.
To elaborate, we know the following three facts:
- Point R is the midpoint of XY, so XR = RY
- Point O is the midpoint of YG, so YO = OG
- Point A is the midpoint of XG, so XA = AG
The diagram shows that YO = 14, so OG must be 14 units long as well.
The diagram also shows XA = 8. Since XA = AG, we know that AG = 8.
-----------------------------
Use this information to find the perimeter of triangle XYG.
Perimeter of XYG = sum of all the sides
Perimeter of XYG = (XY) + (YG) + (XG)
Perimeter of XYG = (22) + (YO+OG) + (XA+AG)
Perimeter of XYG = 22 + (14+14) + (8+8)
Perimeter of XYG = 66
-----------------------------
Then we cut this in half to get the perimeter of triangle ROA.
We do this because each segment of ROA is half that of the corresponding segment of XYG. The midsegments (RA, RO, AO) are cut in half and are parallel to the opposite side.
So,
Perimeter of ROA = (1/2)*(Perimeter of XYG)
Perimeter of ROA = (1/2)*(66)
Perimeter of ROA = 33
