Answer:
ED = 8 units
Step-by-step explanation:
ΔAEB and ΔDEC are similar triangles, hence the ratios of corresponding sides are equal, that is
[tex]\frac{AE}{DE}[/tex] = [tex]\frac{AB}{DC}[/tex], that is
[tex]\frac{2x+4}{x+4}[/tex] = [tex]\frac{9}{6}[/tex] ( cross- multiply )
6(2x + 4) = 9(x + 4) ← distribute parenthesis on both sides
12x + 24 = 9x + 36 ( subtract 9x from both sides )
3x + 24 = 36 ( subtract 24 from both sides )
3x = 12 ( divide both sides by 3 )
x = 4
Hence ED = x + 4 = 4 + 4 = 8 units
