STEP 1: find side $ b $

To find side $ b $ use formula:

$$ A = a \cdot b $$

After substituting $A = 18\, \text{cm}$ and $a = \dfrac{ 16 }{ 5 }\, \text{cm}$ we have:

$$ 18\, \text{cm} = \frac{ 16 }{ 5 }\, \text{cm} \cdot b $$$$ b = \dfrac{ 18\, \text{cm} }{ \frac{ 16 }{ 5 }\, \text{cm} } $$$$ b = \frac{ 45 }{ 8 } $$

STEP 2: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = 2 a + 2 b $$

After substituting $a = \dfrac{ 16 }{ 5 }\, \text{cm}$ and $b = \dfrac{ 45 }{ 8 }\, \text{cm}^0$ we have:

$$ P = 2 \cdot \frac{ 16 }{ 5 }\, \text{cm} + 2 \cdot \frac{ 45 }{ 8 } $$ $$ P = \frac{ 32 }{ 5 }\, \text{cm} + \frac{ 45 }{ 4 } $$ $$ P = \frac{ 353 }{ 20 }\, \text{cm} $$

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