Question

I need some help finding X in similar triangles (See pictures of problems)(98pts)

Answer 1

8/(2x -2) = 14/(3x)

Cross multiply

24x = 28x - 28

Simplify. Isolate the x

24x (-28x) = 28x (-28x) - 28

24x - 28x = -28

-4x = -28

-4x/-4 = -28/-4

x = 6

-----------------------------------------------------------------------------------------------------------------

(x-10)/5 = 39/15

Cross multiply

15(x - 10) = 39(5)

Simplify

15x - 150 = 195

Isolate the x

15x - 150 (+150) = 195 (+150)

15x = 345

15x/15 = 345/15

x = 23

-----------------------------------------------------------------------------------------------------------------

(x + 4)/6 = (2x + 4)/9

Multiply 6 to both sides & 9 to both sides

9(x + 4) = 6(2x + 4)

Distribute 9 to x and 4, and 6 to 2x and 4

9x + 36 = 12x + 24

Isolate the x.

9x (-12x) + 36 (-36) = 12x (-12x) + 24 (-36)

9x - 12x = 24 - 36

-3x = -12

Isolate the x. divide -3 from both sides

-3x/-3 = -12/-3

x = -12/-3

x = 4

-----------------------------------------------------------------------------------------------------------------

hope this helps

Answer 2

Picture 1:

6 + 8 = 14

Smaller Triangle Length - 2(14) - 2 = 26

Larger Triangle Length - 3(14) = 52

Length In Total - 78

x = 14

2nd Picture:

The scale is times 3

So the smaller image is 13 in length (13 * 3 = 39)

To make this possible: 23 - 10 = 13

x = 23

3rd Picture:

9 + 6 = 15

Larger Triangle: 2(15) + 4 = 34

Smaller Triangle: (15) + 4 = 19

Total Length - 53

x = 15

Hope This Helps!