Find the perimeter $ P $ of a rectangle if side $b = 5$ and diagonal $d = 13$.
Answer
$P = 34$
Explanation
STEP 1: find side $ a $
To find side $ a $ use Pythagorean Theorem:
$$ a^2 + b^2 = d^2 $$After substituting $ b = 5 $ and $ d = 13 $ we have:
$$ a ^ {\,2} + 5^2 = 13^2 $$ $$ a ^ {\,2} = 13^2 - 5^2 $$ $$ a ^ {\,2} = 169 - 25 $$ $$ a ^ {\,2} = 144 $$ $$ a = \sqrt{ 144 } $$$$ a = 12 $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 2 a + 2 b $$After substituting $ a = 12 $ and $ b = 5 $ we have:
$$ P = 2 \cdot 12 + 2 \cdot 5 $$ $$ P = 24 + 10 $$ $$ P = 34 $$This page was created using
Rectangle Calculator