According to the midsegment theorem,
midsegment = 1/2 x base of triangle
Looking at the triangle, if IJ is the midsegment, then
IJ = FG/2
FG = 2 x IJ
From the information given,
IJ = 11
FG = 11 x 2 = 22
Also, triangle FGH is similar to triangle IJH. If two triangles are similar, it means that the ratios of their corresponding sides are equal. This means that
FG/IJ = GH/JH = FH/IH
We know that FH = 18 and GH = 21
Thus, we have
22/11 = 18/IH
By crossmultiplying,
22IH = 11 * 18 = 198
IH = 198/22 = 9
Also
22/11 = 21/JH
By crossmultiplying,
22JH = 11 x 21 = 231
JH = 231/22 = 10.5
The perimeter of a triangle is the sum of its sides. The sides of triangle IJH are IJ = 11, IH = 9 and JH = 10.5
Thus,
Perimeter = 11 + 9 + 10.5 = 30.5