Question 821288
That is an isosceles right triangle.
The sides opposite the congruent {{{45^o}}} angles are congruent.
Those are the legs of the right triangle.
If the length of each of those legs is {{{x}}}{{{feet}}} ,
and the hypotenuse measures {{{16feet}}} ,
then according to the Pythagorean theorem
{{{x^2+x^2=16^2}}}
{{{2x^2=16^2}}}
{{{x^2=16^2/2}}}
{{{x^2=(8*2)^2/2}}}
{{{x^2=8^2*2^2/2}}}
{{{x^2=8^2*2}}}
{{{x=sqrt(8^2*2)}}}
{{{x=8sqrt(2)}}}
The, the perimeter is
{{{8sqrt(2)+8sqrt(2)+16=16sqrt(2)+16}}}={{{highlight(16(1+sqrt(2)))}}}={{{highlight(about38.6)}}} (rounded)
So the perimeter is about {{{highlight(38.6feet)}}} .