Question 87592
Given perimeter = 32 cm

perimeter of a square = 4a ( a is the length of the side oa a square)

so 4a = 32

therefore a = 8
{{{ Diagonal^2 = a^2 + a^2}}}(by Pythagorean Theorem)

{{{ Diagonal = sqrt(a^2 + a^2)}}}(by Pythagorean Theorem)

{{{ Diagonal = sqrt(2a^2)}}}

{{{ Diagonal = a*sqrt(2)}}}

Now put the value of a
{{{ Diagonal = 8sqrt(2)}}}

Diagonal = 11.3 cm.