Question

Need help like right now.

Answer 1

Hello from MrBillDoesMath!

Answer:

x = 7

Discussion:

The two triangles are similar by AAA (since the bases of the two triangles are parallel, the base angles in each triangle are identical).  Hence the ratio of corresponding parts are equal. In this case, that mean

(3x-6)  \ ( ( 3x -6) + 12) =  10 \ (10+8)  =>

(3x-6) \ (3x+6) = 10/18 = 5/9.

Multiply both sides by 3x + 6:

(3x -6) \ (3x +6) * (3x + 6) = 5/9 (3x +6) =>

3x -6 = 5/9 (3x +6) =>           (Subtract 5/9 * 3x from both sides)

3x -6 - 5/9(3x) = 5/9*6 =>

3x - 5/9(3x) -6 = 5*6/9 = 30/9 = 10/3 =>

4/9 (3x) -6 = 10/3 =>             (Add 6 to each side)

4/9(3x) = 6 + 10/3 = 28/3 =>

4*(3x)/9 = 28/3   =>              

(12/9) x        = 28/3 =>          (multiply both sides by 9/12)

x = (28/3) * (9/12)  = 252/36 = 126/18 =63/9 = 7

Regards,  

MrB

Answer 2

Let's go:

Big triangle:

12 + 3x - 6 = 3x + 6

10 + 8 = 18

$\frac{10}{18} = \frac{3x - 6}{3x + 6} \\\\ 10.(3x + 6) = 18.(3x - 6) \\\ 30x + 60 = 54x - 108 \\\ 54x - 30x = 60 + 108 \\\ 24x = 168 \\\ x = 7$

I hope I helped you.