[tex] \qquad \: \: \boxed{ \bf{ \: \: AD = 2.4 \: cm \: \: }} \\ \\ [/tex]
Step-by-step explanation:
Given that, In triangle ABC, DE || BC
Further given that,
[tex]\sf \: DB = 7.2 \: cm \\ \\ [/tex]
[tex]\sf \: AE = 1.8 \: cm \\ \\ [/tex]
[tex]\sf \: EC = 5.4 \: cm \\ \\ [/tex]
We know,
Basic Proportionality Theorem :-
This theorem states that, if a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.
[tex]\bf\implies \: \: AD = 2.4 \: cm \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
AdditionalInformation
1. Pythagoras Theorem :-
This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.
2. Converse of Pythagoras Theorem :-
This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.
3. Area Ratio Theorem :-
This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.
Answers & Comments
Verified answer
Answer:
[tex] \qquad \: \: \boxed{ \bf{ \: \: AD = 2.4 \: cm \: \: }} \\ \\ [/tex]
Step-by-step explanation:
Given that, In triangle ABC, DE || BC
Further given that,
[tex]\sf \: DB = 7.2 \: cm \\ \\ [/tex]
[tex]\sf \: AE = 1.8 \: cm \\ \\ [/tex]
[tex]\sf \: EC = 5.4 \: cm \\ \\ [/tex]
We know,
Basic Proportionality Theorem :-
This theorem states that, if a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.
So, using Basic Proportionality Theorem, we have
[tex]\sf \: \dfrac{AD}{DB} = \dfrac{AE}{EC} \\ \\ [/tex]
[tex]\sf \: \dfrac{AD}{7.2} = \dfrac{1.8}{5.4} \\ \\ [/tex]
[tex]\sf \: \dfrac{AD}{7.2} = \dfrac{18}{54} \\ \\ [/tex]
[tex]\sf \: \dfrac{AD}{7.2} = \dfrac{1}{3} \\ \\ [/tex]
[tex]\sf \:AD = \dfrac{7.2}{3} \\ \\ [/tex]
[tex]\bf\implies \: \: AD = 2.4 \: cm \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
1. Pythagoras Theorem :-
This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.
2. Converse of Pythagoras Theorem :-
This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.
3. Area Ratio Theorem :-
This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.