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.