Question

Match the following with the value of $x$, if D and E are the mid points of side AB and AC respectively

• A. 6
• B. 14
• C. 4

Answer 1

In all the figures, D and E are the mid points of side AB and AC respectively as AD = DB and AE = EC.

By Mid point theorem,
$\frac{DE}{BC}=\frac{1}{2}$



From the given figure, $DE=x\text{and}BC=8$
We know, $\frac{DE}{BC}=\frac{1}{2}$
$\Rightarrow \frac{x}{8}=\frac{1}{2}$
$\Rightarrow x=4$



In this figure,
$DE=x\text{and}BC=12$
We know, $\frac{DE}{BC}=\frac{1}{2}$
$\Rightarrow \frac{x}{12}=\frac{1}{2}$
$\Rightarrow x=6$



In the given figure, $DE=7\text{and}BC=x$
We know, $\frac{DE}{BC}=\frac{1}{2}$
$\Rightarrow \frac{7}{x}=\frac{1}{2}$
$\Rightarrow x=14$