Question 283315
Let {{{x = 3+6sqrt(2)}}}
and {{{y = sqrt(8)}}}<br>
With these variables,
perimeter = 2x + 2y
and
area = x*y<br>
Before we start using these formulas, let's simplify y. {{{sqrt(8)}}} has a perfect square factor of 4 so it can be simplified. ({{{sqrt(2)}}} cannot be simplified further.)
{{{y = sqrt(8) = sqrt(4*2) = sqrt(4)*sqrt(2) = 2sqrt(2)}}}<br>
Now let's use the formulas.
Perimeter = 2x + 2y = {{{2(3+6sqrt(2)) + 2(2sqrt(2)) = 6 + 12sqrt(2) + 4sqrt(2) = 6 + 16sqrt(2)}}}
Area = x*y = {{{(3+6sqrt(2))(2sqrt(2)) = 6sqrt(2) + 12*sqrt(2)*sqrt(2) = 6sqrt(2) + 12 * 2 = 6sqrt(2) + 24}}}