STEP 1: find side $ x $

To find side $ x $ use formula:

$$ x = \frac{ a - b } { 2 } $$

After substituting $a = 18\, \text{cm}$ and $b = 10\, \text{cm}$ we have:

$$ x = \frac{ 18\, \text{cm} - 10\, \text{cm} } { 2 } $$ $$ x = \frac{ 8\, \text{cm} } { 2 } $$ $$ x = 4\, \text{cm} $$

STEP 2: find side $ c $

To find side $ c $ use Pythagorean Theorem:

$$ h^2 + x^2 = c^2 $$

After substituting $h = 3\, \text{cm}$ and $x = 4\, \text{cm}$ we have:

$$ \left( 3\, \text{cm} \right)^{2} + \left( 4\, \text{cm} \right)^{2} = c^2 $$ $$ 9\, \text{cm}^2 + 16\, \text{cm}^2 = c^2 $$ $$ c^2 = 25\, \text{cm}^2 $$ $$ c = \sqrt{ 25\, \text{cm}^2 } $$$$ c = 5\, \text{cm} $$

STEP 3: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = a + b + 2 \cdot c $$

After substituting $a = 18\, \text{cm}$, $b = 10\, \text{cm}$ and $c = 5\, \text{cm}$ we have:

$$ P = 18\, \text{cm} + 10\, \text{cm} + 2 \cdot 5\, \text{cm} $$$$ P = 28\, \text{cm} + 10\, \text{cm} $$ $$ P = 38\, \text{cm} $$

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