Question

What is the line segment ET

Answer 1

Side Spitter Theorem : If a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally.

In the given triangle EOG, the line MT cuts the triangle:

According to the side split theorem :

`(EM)/(MG)=(ET)/(TO)`

Substitute the value and solve for x :

`\begin{gathered} (EM)/(MG)=(ET)/(TO) \\ (12)/(6)=(3x-2)/(x+2) \\ \text{Apply cross multiplication:} \\ (2)/(1)=(3x-2)/(x+2) \\ 2(x+2)=3x-2 \\ 2x+4=3x-2 \\ 3x-2x=4+2 \\ x=6 \end{gathered}`

x = 6

Substitute x = 6 in the expression of ET = 3x - 2

ET = 3x - 2

ET = 3(6) - 2

ET = 18 - 2

ET = 16

Answer : The length of the line segment is ET = 16