Find the perimeter $ P $ of a rhombus if diagonal $d_1 = 30$ and diagonal $d_2 = 16$.
Answer
$P = 68$
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 = 30 $ and $ d_2 = 16 $ we have:
$$ 30^2 + 16^2 = 4 \cdot a^2 $$ $$ 900 + 256 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 1156 $$ $$ a^2 = \frac{ 1156 }{ 4 } $$ $$ a^2 = 289 $$ $$ a = \sqrt{ 289 } $$$$ a = 17 $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 4 \cdot a $$After substituting $ a = 17 $ we have:
$$ P = 4 \cdot 17 $$ $$ P = 68 $$This page was created using
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