Answer
a = 5
Work Step by Step
We will use given data about triangle ABC and Pythagoras Theorem to solve for 'a-
We know that -
$c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem)
Therefore -
$a^{2} =c^{2} - b^{2}$
$a^{2} = (13)^{2} - (12)^{2}$
$a^{2} = 169 - 144$
$a^{2} = 25$
therefore $ a = \sqrt (25)$
a = 5
