STEP 1: find side $ b $

To find side $ b $ use formula:

$$ P = 2 a + 2 b $$

After substituting $P = \dfrac{ 11 }{ 2 }\, \text{cm}$ and $a = \dfrac{ 3 }{ 2 }\, \text{cm}$ we have:

$$ \frac{ 11 }{ 2 }\, \text{cm} = 2 \cdot \frac{ 3 }{ 2 }\, \text{cm} + 2 b $$ $$ \frac{ 11 }{ 2 }\, \text{cm} = 3\, \text{cm} + 2 b $$ $$ 2 b = \frac{ 11 }{ 2 }\, \text{cm} - 3\, \text{cm} $$ $$ 2 b = \frac{ 5 }{ 2 }\, \text{cm} $$ $$ b = \dfrac{ \frac{ 5 }{ 2 }\, \text{cm} }{ 2 } $$ $$ b = \frac{ 5 }{ 4 }\, \text{cm} $$

STEP 2: find diagonal $ d $

To find diagonal $ d $ use Pythagorean Theorem:

$$ a^2 + b^2 = d^2 $$

After substituting $a = \dfrac{ 3 }{ 2 }\, \text{cm}$ and $b = \dfrac{ 5 }{ 4 }\, \text{cm}$ we have:

$$ \left( \frac{ 3 }{ 2 }\, \text{cm} \right)^{2} + \left( \frac{ 5 }{ 4 }\, \text{cm} \right)^{2} = d^2 $$ $$ \frac{ 9 }{ 4 }\, \text{cm}^2 + \frac{ 25 }{ 16 }\, \text{cm}^2 = d^2 $$ $$ d^2 = \frac{ 61 }{ 16 }\, \text{cm}^2 $$ $$ d = \sqrt{ \frac{ 61 }{ 16 }\, \text{cm}^2 } $$$$ d = \frac{\sqrt{ 61 }}{ 4 }\, \text{cm} $$

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