Find the side $ a $ of a rhombus if area $A = 480$ and diagonal $d_2 = 48$.

$a = 26$

STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$

After substituting $ A = 480 $ and $ d_2 = 48 $ we have:

$$ 480 = \dfrac{ d_1 \cdot 48 }{ 2 } $$$$ 480 \cdot 2 = d_1 \cdot 48 $$$$ 960 = 48 \cdot d_1 $$$$ d_1 = \dfrac{ 960}{ 48 } $$$$ d_1 = 20 $$

STEP 2: find side $ a $

To find side $ a $ use formula:

$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$

After substituting $ d_1 = 20 $ and $ d_2 = 48 $ we have:

$$ 20^2 + 48^2 = 4 \cdot a^2 $$ $$ 400 + 2304 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 2704 $$ $$ a^2 = \frac{ 2704 }{ 4 } $$ $$ a^2 = 676 $$ $$ a = \sqrt{ 676 } $$$$ a = 26 $$

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