Question

Find $AD$ with the help of Apollonius theorem, where $△ABC$ is equilateral with side $=5$ cm.

• A. $2$ cm
• B. $4.33$ cm
• C. $6$ cm
• D. $2.5$ cm

Answer 1

The correct option is B $4.33$ cm

From figure, we have

$A{B}^2+A{C}^2=2(C{D}^2+A{D}^2)$

$\Rightarrow \frac{5^2+5^2}{2}=C{D}^2+A{D}^2$
$\Rightarrow \frac{50}{2}=25=(2.5{)}^2+A{D}^2$

$\Rightarrow 25-(2.5{)}^2=A{D}^2,A{D}^2=25-6.25$

Thus, $A{D}^2=18.75$

$\Rightarrow AD=4.33$