Answer:
11) x = 8
12)x = 4
Step-by-step explanation:
In similar triangles,
11) ΔABC ~ ΔDEC
[tex]\sf \dfrac{AB}{DE} = \dfrac{AC}{DC}\\\\\\ \dfrac{30}{18}= \dfrac{2x - 1 }{x+ 1}[/tex]
Cross multiply,
30*(x +1) = 18*(2x - 1)
30x +30 = 18*2x - 18
30x +30 = 36x - 18
Add 18 to both sides,
30x + 30 + 18 = 36x
30x + 48 = 36x
Subtract 30x from both sides,
48 = 36x - 30x
48 = 6x
Divide both sides by 6,
48 ÷ 6 = x
[tex]\boxed{\bf x = 8}[/tex]
12) ΔABC ~ ΔDEC
[tex]\sf \dfrac{AB}{DE} = \dfrac{AC}{DC}\\\\\\ \dfrac{6x - 2 }{2x + 8}= \dfrac{ 5.5 }{4}[/tex]
Cross multiply,
4*(6x - 2) = 5.5*(2x + 8)
4*6x - 4*2 = 5.5*2x + 5.5*8
24x - 8 = 11x + 44
Add 8 to both sides,
24x = 11x + 44 + 8
24x = 11x + 52
Subtract 11x from both sides,
24x - 11x = 52
13x = 52
Divide both sides by 13,
x = 52 ÷ 13
[tex]\boxed{\bf x = 4}[/tex]