STEP 1: find side $ x $

To find side $ x $ use formula:

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

After substituting $a = 5\, \text{cm}$ and $b = 4\, \text{cm}$ we have:

$$ x = \frac{ 5\, \text{cm} - 4\, \text{cm} } { 2 } $$ $$ x = \frac{ 1\, \text{cm} } { 2 } $$ $$ x = \frac{ 1 }{ 2 }\, \text{cm} $$

STEP 2: find height $ h $

To find height $ h $ use Pythagorean Theorem:

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

After substituting $x = \dfrac{ 1 }{ 2 }\, \text{cm}$ and $c = 3\, \text{cm}$ we have:

$$ h ^ {\,2} + \left( \frac{ 1 }{ 2 }\, \text{cm} \right)^{2} = \left( 3\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = \left( 3\, \text{cm} \right)^{2} - \left( \frac{ 1 }{ 2 }\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 9\, \text{cm}^2 - \frac{ 1 }{ 4 }\, \text{cm}^2 $$ $$ h ^ {\,2} = \frac{ 35 }{ 4 }\, \text{cm}^2 $$ $$ h = \sqrt{ \frac{ 35 }{ 4 }\, \text{cm}^2 } $$$$ h = \frac{\sqrt{ 35 }}{ 2 }\, \text{cm} $$

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