Answer :

anbu40

Answer:

11) x = 8

12)x = 4

Step-by-step explanation:

In similar triangles,

  • Corresponding angles are congruent.
  • corresponding sides are in same proportion.

   

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]