Find the height $ h $ of a rhombus if side $a = 13$ and diagonal $d_1 = 24$.

$h = \frac{ 120 }{ 13 }$

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 = 24 $ and $ a = 13 $ we have:

$$ 24^2 + d_2^2 = 4 \cdot 13^2 $$ $$ 576 + d_2^2 = 676 $$ $$ d_2^2 = 676 - 576 $$ $$ d_2^2 = 100 $$ $$ d_2 = \sqrt{ 100 } $$$$ d_2 = 10 $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ d_1 = 24 $ and $ d_2 = 10 $ we have:

$$ A = \dfrac{ 24 \cdot 10 }{ 2 }$$$$ A = \dfrac{ 240 }{ 2 } $$$$ A = 120 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

$$ A = a \cdot h $$

After substituting $ A = 120 $ and $ a = 13 $ we have:

$$ 120 = 13 \cdot h $$$$ h = \dfrac{ 120 }{ 13 } $$$$ h = \frac{ 120 }{ 13 } $$

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