STEP 1: find side $ x $
To find side $ x $ use formula:
$$ x = \frac{ a - b } { 2 } $$After substituting $ a = 5 $ and $ b = 4 $ we have:
$$ x = \frac{ 5 - 4 } { 2 } $$ $$ x = \frac{ 1 } { 2 } $$ $$ x = \frac{ 1 }{ 2 } $$STEP 2: find height $ h $
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + x^2 = c^2 $$After substituting $ x = \frac{ 1 }{ 2 } $ and $ c = 3 $ we have:
$$ h ^ {\,2} + \left(\frac{ 1 }{ 2 }\right)^2 = 3^2 $$ $$ h ^ {\,2} = 3^2 - \left(\frac{ 1 }{ 2 }\right)^2 $$ $$ h ^ {\,2} = 9 - \frac{ 1 }{ 4 } $$ $$ h ^ {\,2} = \frac{ 35 }{ 4 } $$ $$ h = \sqrt{ \frac{ 35 }{ 4 } } $$$$ h = \frac{\sqrt{ 35 }}{ 2 } $$