Question

In the given figure $ DE\left|\right|BC$. Find $ EC$.

1.5 cm D 1cm E C 

Answer 1

Step 1: State the given data and the basic proportionality theorem

In the adjoining figure, it is given that,

$$\begin{gathered} AD=1.5cm \\ DB=3cm \\ AE=1cm \end{gathered}$$

And, $DE\left|\right|BC$

Now, as we know, the basic proportionality theorem of triangles states that,

“If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.”

Step 2: Apply the basic proportionality theorem

Now, since $DE\left|\right|BC$ in $△ABC$,

So, $\frac{AD}{DB}=\frac{AE}{EC}$

$\Rightarrow$ $\frac{1.5}{3}=\frac{1}{EC}$

$\Rightarrow$ $1.5\times EC=1\times 3$ [by cross-multiplication]

$\Rightarrow$ $EC=\frac{1\times 3}{1.5}$

$\Rightarrow$ $EC=\frac{1\times 3}{1.5}\times \frac{10}{10}$

$\Rightarrow$ $EC=\frac{30}{15}$ $\left[\because \frac{a}{b}\times \frac{c}{d}=\frac{a\times c}{b\times d}\right]$

$\Rightarrow$ $EC=2$

Hence, the required value of $EC$ is $2cm$.