Answer:
Please see details below
Explanation:
Notice that since you have drawn mid-segments for all sides of the triangles, the three smaller triangles generated at the vertices, are all similar triangles to the large one (XYW).
Let's look at what happens with the smaller triangles:
Triangle QXR is similar to XYW, since the side QR has to be parallel to the big side WY. By construction, the side XQ is half of the side XW, therefore all sides of the smaller triangle *QXR formed must maintain the same proportion. Then side QR is half of side WY which makes side WY = 2 (2.93 cm) = 5.86 cm.
The same reasoning is valid when we compare triangle RYS with the larger triangle XYW: side RS of the small triangle is half of side XW of the large triangle, That is: XW = 2 (2.04 cm) = 4.08 cm
Similarly, small triangle SWQ is similar to XYW, and the side QS has to be half of side XY, therefore side XY = 2 (2.28 cm) = 4.56 cm
Then, the perimeter of triangle XYW is:
XY + YW + XW= 4.56 cm + 5.86 cm + 4.08 cm = 14.5 cm