Question
Find the diagonal $ d $ of a rectangle if side $a = 8\, \text{cm}$ and side $b = 6 \sqrt{ 5 }\, \text{cm}$.
Answer
$2 \sqrt{ 61 }\, \text{cm}$
Explanation
To find diagonal $ d $ use Pythagorean Theorem:
$$ a^2 + b^2 = d^2 $$After substituting $a = 8\, \text{cm}$ and $b = 6 \sqrt{ 5 }\, \text{cm}$ we have:
$$ \left( 8\, \text{cm} \right)^{2} + \left( 6 \sqrt{ 5 }\, \text{cm} \right)^{2} = d^2 $$ $$ 64\, \text{cm}^2 + 180\, \text{cm}^2 = d^2 $$ $$ d^2 = 244\, \text{cm}^2 $$ $$ d = \sqrt{ 244\, \text{cm}^2 } $$$$ d = 2 \sqrt{ 61 }\, \text{cm} $$This page was created using
Rectangle Calculator