Find the perimeter $ P $ of a rhombus if diagonal $d_1 = 16$ and diagonal $d_2 = 12$.
Answer
$P = 40$
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 = 16 $ and $ d_2 = 12 $ we have:
$$ 16^2 + 12^2 = 4 \cdot a^2 $$ $$ 256 + 144 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 400 $$ $$ a^2 = \frac{ 400 }{ 4 } $$ $$ a^2 = 100 $$ $$ a = \sqrt{ 100 } $$$$ a = 10 $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 4 \cdot a $$After substituting $ a = 10 $ we have:
$$ P = 4 \cdot 10 $$ $$ P = 40 $$This page was created using
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