Question
In a right triangle $ABC$, $\angle B = 90^{\circ}$. If $AC = 13\ cm, BC = 5\ cm$, find $AB$.
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Answer
It is given that $\triangle \mathrm{ABC}$ is right-angled at $B$
Pythagoras Theorem: In a right angles triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
Therefore, by using Pythagoras theorem, we get:
$A C^{2}=A B^{2}+B C^{2}$
$13 ^{2}={AB}^{2}+5^{2}$
$\Rightarrow$$\mathrm{AB}^{2}=169 -25 $
$\mathrm{AB}^{2}=144 $
$\Rightarrow$$\mathrm{AB}=\sqrt{144} $
$AB = 12$
Therefore, $AB = 12\ cm$
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