Question

In a figure \[DE||BC\] then find EC and AD?

Answer 1

Hint: Here the question is related to the geometry and there is a line which is parallel to the base of the triangle. So there is a theorem when a line is parallel to the line of the triangle then their sides are proportional. Hence by using the simple arithmetic operations we can solve the given question.

Complete step-by-step answer:
I.A triangle is a plane figure which has 3 sides. When a parallel line is drawn to the triangle then we can form two triangles. These triangles look to be similar. Hence we can call it similar triangles. Then there is a property for the similar triangles that is there’s sides are proportional.
Now we consider the first problem.
The line DE is parallel to the BC. Therefore we have two triangles namely, \[\vartriangle ADE\] and \[\vartriangle ABC\]
These triangles are similar.
If the triangles are similar then their sides are proportional. So now we have
\[\dfrac{{AD}}{{DB}} = \dfrac{{AE}}{{EC}}\]
On substituting the values by considering the diagram we have
\[ \Rightarrow \dfrac{{1.5}}{3} = \dfrac{1}{{EC}}\]
On cross multiplying we have
\[ \Rightarrow EC \times 1.5 = 3 \times 1\]
On simplifying we have
\[ \Rightarrow EC \times 1.5 = 3\]
On dividing by 1.5 we have
\[ \Rightarrow EC = 2\]
Therefore the value of EC = 2 cm.
So, the correct answer is “ EC = 2 cm”.

II.Now we consider the second problem.
The line DE is parallel to the BC. Therefore we have two triangles namely, \[\vartriangle ADE\] and \[\vartriangle ABC\]
These triangles are similar.
If the triangles are similar then their sides are proportional. So now we have
\[\dfrac{{AD}}{{DB}} = \dfrac{{AE}}{{EC}}\]
On substituting the values by considering the diagram we have
\[ \Rightarrow \dfrac{{AD}}{{7.2}} = \dfrac{{1.8}}{{5.4}}\]
On cross multiplying we have
\[ \Rightarrow AD \times 5.4 = 1.8 \times 7.2\]
On simplifying we have
\[ \Rightarrow AD \times 5.4 = 12.96\]
On dividing by 5.4 we have
\[ \Rightarrow EC = 2.4\]
Therefore the value of AD = 2.4 cm.
So, the correct answer is “AD = 2.4 cm”.

Note: To solve these kinds of problems we have to know about the properties of the triangles. Some triangles are similar congruent etc., and they have some specific properties. To simplify we need the arithmetic operations and the tables of multiplication is needed.