STEP 1: find side $ a $
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 24 $ and $ s = 25 $ we have:
$$ 24^2 + \frac{ a^2 }{ 4 } = 25^2 $$ $$ \frac{ a^2 }{ 4 } = 25^2 - 24^2 $$ $$ \frac{ a^2 }{ 4 } = 625 - 576 $$ $$ a^2 = 49 \cdot 4 $$ $$ a^2 = 196 $$ $$ a = \sqrt{ 196 } $$$$ a = 14 $$STEP 2: find lateral edge $ e $
To find lateral edge $ e $ use Pythagorean Theorem:
$$ s^2 + \frac{ a^2 }{ 4 } = e^2 $$After substituting $ s = 25 $ and $ a = 14 $ we have:
$$ 25^2 + \frac{ 14^2 }{ 4 }= e^2 $$ $$ 625 + \frac{ 196 }{ 4 }= e^2 $$ $$ 625 + 49 = e^2 $$ $$ e^2 = 674 $$ $$ e = \sqrt{ 674 } $$