STEP 1: find side $ a $

To find side $ a $ use formula:

$$ r = \dfrac{ a }{ 2 } $$

After substituting $r = 60\, \text{cm}$ we have:

$$ 60\, \text{cm} = \dfrac{ a }{ 2 } $$ $$ a = 60\, \text{cm} \cdot 2 $$ $$ a = 120\, \text{cm} $$

STEP 2: find height $ h $

To find height $ h $ use Pythagorean Theorem:

$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$

After substituting $a = 120\, \text{cm}$ and $s = 36\, \text{cm}$ we have:

$$ h ^ {\,2} + \frac{ \left( 120\, \text{cm} \right)^{2} }{ 4 } = \left( 36\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 14400\, \text{cm}^2 }{ 4 } = \left( 36\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + 3600\, \text{cm}^2 = \left( 36\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 1296\, \text{cm}^2 - 3600\, \text{cm}^2 $$ $$ h ^ {\,2} = -2304\, \text{cm}^2 $$

This equation has no solution $ \Longrightarrow $ The problem has no solution.

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