Find the perimeter $ P $ of a rhombus if diagonal $d_1 = 12$ and diagonal $d_2 = 9$.
Answer
$P = 30$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 12 $ and $ d_2 = 9 $ we have:
$$ 12^2 + 9^2 = 4 \cdot a^2 $$ $$ 144 + 81 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 225 $$ $$ a^2 = \frac{ 225 }{ 4 } $$ $$ a^2 = \frac{ 225 }{ 4 } $$ $$ a = \sqrt{ \frac{ 225 }{ 4 } } $$$$ a = \frac{ 15 }{ 2 } $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 4 \cdot a $$After substituting $ a = \frac{ 15 }{ 2 } $ we have:
$$ P = 4 \cdot \frac{ 15 }{ 2 } $$ $$ P = 30 $$This page was created using
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