Answer
427.5k+ views
Hint: First we have to see the figure clearly.
The line divides the triangle into two proportions.
The side of triangles has values.
From the given triangle, we get the values and then we applied in proportionality theorem
Finally, we can find the value of $X$.
Formula used: Triangle proportionality theorem: If a line parallel to one side of a triangle intersects the other sides, then it divides those sides proportionally.
If $\overline {DE} $ is parallel to $\overline {AC} $, then $\dfrac{{BD}}{{DA}} = \dfrac{{BE}}{{EC}}$
Complete step-by-step answer:
In this figure a line segment is drawn parallel to one side of the triangle and the lengths of certain line segments are marked.
(i) In the triangle applying proportionality theorem on their sides we get,
\[\dfrac{1}{c} = \dfrac{d}{{\mathbf{x}}}\]
By Cross multiplication we get,
\[ \Rightarrow {\mathbf{x}} = cd\]
Therefore, the value of $X$ is \[cd\]
(ii) In the triangle applying proportionality theorem on their sides we get,
\[\dfrac{a}{1} = \dfrac{b}{{\mathbf{x}}}\]
By Cross multiplication we get
\[ \Rightarrow {\mathbf{x}} = \dfrac{b}{a}\]
Therefore, the value of $X$ is \[\dfrac{b}{a}\]
(iii) In the triangle applying proportionality theorem on their sides we get,
\[\dfrac{1}{g} = \dfrac{g}{{\mathbf{x}}}\]
By Cross multiplication we get
\[ \Rightarrow {\mathbf{x}} = {g^2}\]
Therefore, the value of $X$ is \[{g^2}\]
(iv) In the triangle applying proportionality theorem on their sides we get,
\[\dfrac{1}{{\mathbf{x}}} = \dfrac{h}{1}\]
By Cross multiplication we get,
\[ \Rightarrow {\mathbf{x}} = \dfrac{1}{h}\]
Therefore, the value of $X$ is \[\dfrac{1}{h}\]
Note: The converse of the proportionality theorem is also true.
If a line divides two sides of a triangle proportionally then it is parallel to the third side of the triangle.
If $\dfrac{{BD}}{{DA}} = \dfrac{{BE}}{{EC}}$ then,$\overline {DE} $ is parallel to $\overline {AC} $.
The line divides the triangle into two proportions.
The side of triangles has values.
From the given triangle, we get the values and then we applied in proportionality theorem
Finally, we can find the value of $X$.
Formula used: Triangle proportionality theorem: If a line parallel to one side of a triangle intersects the other sides, then it divides those sides proportionally.
![seo images](https://www.vedantu.com/question-sets/9f139c4e-6ce5-4e6a-b4a8-c3f17f2597b91599490056021044338.png)
If $\overline {DE} $ is parallel to $\overline {AC} $, then $\dfrac{{BD}}{{DA}} = \dfrac{{BE}}{{EC}}$
Complete step-by-step answer:
In this figure a line segment is drawn parallel to one side of the triangle and the lengths of certain line segments are marked.
(i) In the triangle applying proportionality theorem on their sides we get,
\[\dfrac{1}{c} = \dfrac{d}{{\mathbf{x}}}\]
By Cross multiplication we get,
\[ \Rightarrow {\mathbf{x}} = cd\]
Therefore, the value of $X$ is \[cd\]
(ii) In the triangle applying proportionality theorem on their sides we get,
\[\dfrac{a}{1} = \dfrac{b}{{\mathbf{x}}}\]
By Cross multiplication we get
\[ \Rightarrow {\mathbf{x}} = \dfrac{b}{a}\]
Therefore, the value of $X$ is \[\dfrac{b}{a}\]
(iii) In the triangle applying proportionality theorem on their sides we get,
\[\dfrac{1}{g} = \dfrac{g}{{\mathbf{x}}}\]
By Cross multiplication we get
\[ \Rightarrow {\mathbf{x}} = {g^2}\]
Therefore, the value of $X$ is \[{g^2}\]
(iv) In the triangle applying proportionality theorem on their sides we get,
\[\dfrac{1}{{\mathbf{x}}} = \dfrac{h}{1}\]
By Cross multiplication we get,
\[ \Rightarrow {\mathbf{x}} = \dfrac{1}{h}\]
Therefore, the value of $X$ is \[\dfrac{1}{h}\]
Note: The converse of the proportionality theorem is also true.
If a line divides two sides of a triangle proportionally then it is parallel to the third side of the triangle.
If $\dfrac{{BD}}{{DA}} = \dfrac{{BE}}{{EC}}$ then,$\overline {DE} $ is parallel to $\overline {AC} $.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)