Answer:
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,
[tex]\frac{Length\ of\ AD}{Length\ of\ DC} =\frac{Length\ of\ BE}{Length\ of\ EC}[/tex]
On substituting the given values, we get;
[tex]\frac{x}{12} = \frac{x+6}{16}[/tex]
By using Cross multiplication method we get;
[tex]16x=12(x+6)[/tex]
Now Using Distributive Property we get;
[tex]16x=12x+72[/tex]
Using Subtraction Property We will subtract both side by 12x;
[tex]16x-12x=12x+72-12x\\\\4x=72[/tex]
Now Using Division property we will divide both side by 4 we get;
[tex]\frac{4x}{4} =\frac{72}{4} \\\\x= 18[/tex]
Hence The value of x is 18.
