Question

In the figure below, the segment is parallel to one side of the triangle. x=

1.5
18
24
15

Answer 1

18

Explanation:

Answer 2

The Value of x is 18.

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,

`(Length\ of\ AD)/(Length\ of\ DC) =(Length\ of\ BE)/(Length\ of\ EC)`

On substituting the given values, we get;

`(x)/(12) = (x+6)/(16)`

By using Cross multiplication method we get;

`16x=12(x+6)`

Now Using Distributive Property we get;

`16x=12x+72`

Using Subtraction Property We will subtract both side by 12x;

`16x-12x=12x+72-12x\\\\4x=72`

Now Using Division property we will divide both side by 4 we get;

`(4x)/(4) =(72)/(4) \\\\x= 18`

Hence The value of x is 18.