Applying the triangle proportionality theorem, the value of x in the triangles shown is: x = 8.
What is the triangle proportionality theorem?
The theorem of triangle proportionality asserts that when a line intersects two sides of a triangle and runs parallel to the third side, it divides those sides proportionally.
To find x, we would apply this theorem since triangles KLM and KHJ are similar triangles:
KL/KH = LM/HJ
Given that:
KL = x
KH = 4
LM = 24
HJ = 12
Substitute:
x/4 = 24/12
x/4 = 2/1
x = 8