The Value of x is 18.
Step-by-step explanation:
Firstly we redraw the given triangle with nomenclature.
You can find the triangle in attachment.
So we have a triangle ABC in which D and E are the points of intersection of side AC and BC respectively.
And also given that DE is parallel to AB.
Length of AD = x
Length of DC = 12
Length of BE = x+6
Length of EC = x
We have to find the value of 'x'.
Now according to proportionality theorem of triangle, which states that;
"If a line drawn parallel to one side of a triangle intersects the other two sides of the triangle then it divides the remaining two sides into proportion."
Hence,
On substituting the given values, we get;
By using Cross multiplication method we get;
Now Using Distributive Property we get;
Using Subtraction Property We will subtract both side by 12x;
Now Using Division property we will divide both side by 4 we get;
Hence The value of x is 18.