Triangles EGF and DEF are similar with sides in proportion:
EF/GF = DE/EG. Solving, x = 19. Measure of EH = 28 inches (x+5 + 9).
Similar triangles:
Triangles EGF and DEF are similar because they have two pairs of corresponding sides proportional and the corresponding angles equal.
Proportionality of sides:
EF/GF = DE/EG
12/x+5 = 6/9
Solving for x:
x+5 = 24
x = 19
Measure of EH:
EH = FG + GH
EH = x+5 + 9
EH = 19 + 9
EH = 28 inches
Therefore, the measure of the triangle is 28 inches.