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In $\triangle ABC,\:\angle B$ is a right angle, AC = $6$ cm, and D is the mid-point of $AC$. The length of $BD$ is ___________

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Given that, 

  • $AB=6$ cm.
  • $BC=8$ cm.
  • $\angle ABC=90^\circ$.

In $\triangle ABC,$ we can apply the pythagorean theorem.

$(AC)^{2}=(AB)^{2}+(BC)^{2}$

$\Rightarrow (AC)^{2}=6^{2}+8^{2}$

$\Rightarrow (AC)^{2}=36+64$

$\Rightarrow (AC)^{2}=100$

$\Rightarrow \boxed{AC=10\text{cm}}$.

$D$ is the mid point of $AC$, thus $AD=DC=\frac{10}{2}=5$ cm.

Also, $(BD)^{2}=(AD)\times(DC)$ 

$\Rightarrow (BD)^{2}=5\times5=25$.

$\Rightarrow \boxed{BD=5\text{cm}}$.

$\therefore$ The length of $BD$ is $5$ cm.

Correct Answer : $5$

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