Question 847873
Let the width be x.  Then length is 3x.

Notice that when we take two sides with its diagonal we have a right triangle.

Apply pythagorean theorem.

{{{x^2 + (3x)^2 = (6*sqrt(10))^2}}}

{{{x^2 + 9x^2 = 360}}}

{{{10x^2 = 360}}}

{{{x^2 = 36}}}

{{{x=6}}} <---width

Then our length is 18.


P = 2L + 2W

P = 2(6) + 2(18) = {{{highlight(48)}}} cm