Triangle HIJ is similar to triangle LMN. Side LM measures x + 1, side MN measures 2x and side NL measures 3x – 1. Side HI measures 12 and side JH measures 26.4. Find the value of x

12/26.4 = (x+1)/(3x-1)

36 -12 x = 26.4 x + 26.4 etc

To find the value of x, we can set up a proportion using the corresponding sides of the similar triangles.

The corresponding sides of similar triangles are in proportion to each other. Therefore, we can set up the following proportion:

LM / HI = MN / HJ

Substituting the given values:

(x + 1) / 12 = 2x / 26.4

Cross-multiplying:

12 * 2x = 26.4 * (x + 1)

24x = 26.4x + 26.4

Combine like terms:

24x - 26.4x = 26.4

-2.4x = 26.4

Dividing both sides by -2.4:

x = 26.4 / -2.4

x ≈ -11

Therefore, the value of x is approximately -11.