Question 829785
x length
w width


{{{x=2w}}};
Perimeter information means {{{2x+2w=66}}}
{{{x+w=33}}}
{{{2w+w=33}}}, when substituted for x.
{{{3w=33}}}
{{{highlight(w=11)}}}
'
{{{x=2w}}}
{{{x=2*11}}}
{{{highlight(x=22)}}}
'
The diagonal is hypotenuse of the triangle having sides 11 and 22.
Use Pythagorean Theorem:
{{{h^2=11^2+22^2}}}
{{{h=sqrt(11^2+22^2)}}}
{{{h=sqrt(121+484)}}}
{{{h=sqrt(605)}}}
{{{highlight(h=11*sqrt(5))}}}, the diagonal