STEP 1: find side $ a $

To find side $ a $ use Pythagorean Theorem:

$$ a^2 + b^2 = d^2 $$

After substituting $b = 5\, \text{cm}$ and $d = 13\, \text{cm}$ we have:

$$ a ^ {\,2} + \left( 5\, \text{cm} \right)^{2} = \left( 13\, \text{cm} \right)^{2} $$ $$ a ^ {\,2} = \left( 13\, \text{cm} \right)^{2} - \left( 5\, \text{cm} \right)^{2} $$ $$ a ^ {\,2} = 169\, \text{cm}^2 - 25\, \text{cm}^2 $$ $$ a ^ {\,2} = 144\, \text{cm}^2 $$ $$ a = \sqrt{ 144\, \text{cm}^2 } $$$$ a = 12\, \text{cm} $$

STEP 2: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = 2 a + 2 b $$

After substituting $a = 12\, \text{cm}$ and $b = 5\, \text{cm}$ we have:

$$ P = 2 \cdot 12\, \text{cm} + 2 \cdot 5\, \text{cm} $$ $$ P = 24\, \text{cm} + 10\, \text{cm} $$ $$ P = 34\, \text{cm} $$

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