a, b - стороны прямоугольника, тогда 
1)
b =\frac{P-2a}{2}= \frac{16-2*5}{2} = 3 => d=\sqrt{a^2+b^2} = \sqrt{5^2+3^2} = \sqrt{34}" alt="P=16 => b =\frac{P-2a}{2}= \frac{16-2*5}{2} = 3 => d=\sqrt{a^2+b^2} = \sqrt{5^2+3^2} = \sqrt{34}" align="absmiddle" class="latex-formula">
2)
b =\frac{P-2a}{2}= \frac{10 +10\sqrt{3}-2*5}{2} = 5\sqrt{3} => d=\sqrt{a^2+b^2} = \sqrt{5^2+(5\sqrt{3})^2} = 10" alt="P=10 +10\sqrt{3} => b =\frac{P-2a}{2}= \frac{10 +10\sqrt{3}-2*5}{2} = 5\sqrt{3} => d=\sqrt{a^2+b^2} = \sqrt{5^2+(5\sqrt{3})^2} = 10" align="absmiddle" class="latex-formula">
3)
b=\sqrt{d^2 - a^2}= \sqrt{169 - 25} = \sqrt{144} = 12 => P = 2a+2b =2*5+2*12 = 34" alt="d=13 => b=\sqrt{d^2 - a^2}= \sqrt{169 - 25} = \sqrt{144} = 12 => P = 2a+2b =2*5+2*12 = 34" align="absmiddle" class="latex-formula">
4)
b=\sqrt{d^2 - a^2}= \sqrt{39 - 25} = \sqrt{14} => P = 2a+2b =2*5+2*\sqrt{14} = 10 + 2*\sqrt{14}" alt="d=8 => b=\sqrt{d^2 - a^2}= \sqrt{39 - 25} = \sqrt{14} => P = 2a+2b =2*5+2*\sqrt{14} = 10 + 2*\sqrt{14}" align="absmiddle" class="latex-formula">