Find the height $ h $ of a rhombus if side $a = 17$ and diagonal $d_1 = 30$.

$h = \frac{ 240 }{ 17 }$

STEP 1: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

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

After substituting $ d_1 = 30 $ and $ a = 17 $ we have:

$$ 30^2 + d_2^2 = 4 \cdot 17^2 $$ $$ 900 + d_2^2 = 1156 $$ $$ d_2^2 = 1156 - 900 $$ $$ d_2^2 = 256 $$ $$ d_2 = \sqrt{ 256 } $$$$ d_2 = 16 $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ d_1 = 30 $ and $ d_2 = 16 $ we have:

$$ A = \dfrac{ 30 \cdot 16 }{ 2 }$$$$ A = \dfrac{ 480 }{ 2 } $$$$ A = 240 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

$$ A = a \cdot h $$

After substituting $ A = 240 $ and $ a = 17 $ we have:

$$ 240 = 17 \cdot h $$$$ h = \dfrac{ 240 }{ 17 } $$$$ h = \frac{ 240 }{ 17 } $$

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