Find the perimeter $ P $ of a rhombus if diagonal $d_1 = 5$ and diagonal $d_2 = 5$.
Answer
$P = 10 \sqrt{ 2 }$
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 = 5 $ and $ d_2 = 5 $ we have:
$$ 5^2 + 5^2 = 4 \cdot a^2 $$ $$ 25 + 25 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 50 $$ $$ a^2 = \frac{ 50 }{ 4 } $$ $$ a^2 = \frac{ 25 }{ 2 } $$ $$ a = \sqrt{ \frac{ 25 }{ 2 } } $$$$ a = \frac{ 5 \sqrt{ 2}}{ 2 } $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 4 \cdot a $$After substituting $ a = \frac{ 5 \sqrt{ 2}}{ 2 } $ we have:
$$ P = 4 \cdot \frac{ 5 \sqrt{ 2}}{ 2 } $$ $$ P = 10 \sqrt{ 2 } $$This page was created using
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