Find the perimeter $ P $ of a rectangle if side $b = 4$ and diagonal $d = 55$.
Answer
$P = 117.7087$
Explanation
STEP 1: find side $ a $
To find side $ a $ use Pythagorean Theorem:
$$ a^2 + b^2 = d^2 $$After substituting $ b = 4 $ and $ d = 55 $ we have:
$$ a ^ {\,2} + 4^2 = 55^2 $$ $$ a ^ {\,2} = 55^2 - 4^2 $$ $$ a ^ {\,2} = 3025 - 16 $$ $$ a ^ {\,2} = 3009 $$ $$ a = \sqrt{ 3009 } $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 2 a + 2 b $$After substituting $ a = \sqrt{ 3009 } $ and $ b = 4 $ we have:
$$ P = 2 \cdot \sqrt{ 3009 } + 2 \cdot 4 $$ $$ P = 2 \sqrt{ 3009 } + 8 $$ $$ P = 117.7087 $$This page was created using
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