Find the perimeter $ P $ of a rhombus if diagonal $d_1 = 18$ and diagonal $d_2 = 12$.
Answer
$P = 12 \sqrt{ 13 }$
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 = 18 $ and $ d_2 = 12 $ we have:
$$ 18^2 + 12^2 = 4 \cdot a^2 $$ $$ 324 + 144 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 468 $$ $$ a^2 = \frac{ 468 }{ 4 } $$ $$ a^2 = 117 $$ $$ a = \sqrt{ 117 } $$$$ a = 3 \sqrt{ 13 } $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 4 \cdot a $$After substituting $ a = 3 \sqrt{ 13 } $ we have:
$$ P = 4 \cdot 3 \sqrt{ 13 } $$ $$ P = 12 \sqrt{ 13 } $$This page was created using
Rhombus Calculator