Find the height $ h $ of a rhombus if side $a = 200$ and diagonal $d_1 = \frac{ 2877359 }{ 10000 }$.

$h = 199.8782$

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 = \frac{ 2877359 }{ 10000 } $ and $ a = 200 $ we have:

$$ \left(\frac{ 2877359 }{ 10000 }\right)^2 + d_2^2 = 4 \cdot 200^2 $$ $$ 82791.9481 + d_2^2 = 160000 $$ $$ d_2^2 = 160000 - 82791.9481 $$ $$ d_2^2 = 77208.0519 $$ $$ d_2 = \sqrt{ 77208.0519 } $$$$ d_2 = 277.8634 $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ d_1 = \frac{ 2877359 }{ 10000 } $ and $ d_2 = 277.8634 $ we have:

$$ A = \dfrac{ \frac{ 2877359 }{ 10000 } \cdot 277.8634 }{ 2 }$$$$ A = \dfrac{ 79951.2666 }{ 2 } $$$$ A = 39975.6333 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

$$ A = a \cdot h $$

After substituting $ A = 39975.6333 $ and $ a = 200 $ we have:

$$ 39975.6333 = 200 \cdot h $$$$ h = \dfrac{ 39975.6333 }{ 200 } $$$$ h = 199.8782 $$

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