Помогите геометрия!!!!!!!

$\left \{ {{ \sqrt{a^2+b^2}=2 \sqrt{10} } \atop {ab=12}} \right. \\\ \left \{ {{ a^2+b^2=40 } \atop {a= \frac{12}{b} }} \right. \\\ ( \frac{12}{b})^2+b^2=40 \\\ \frac{144}{b^2}+b^2=40 \\\ b^4-40b^2+144=0 \\\ D_1=20^2-144=256 \\\ b^2= 20-16=4\Rightarrow b_1=2 \\\ b^2= 20+16=36\Rightarrow b_2=6 \\\ a_1= \frac{12}{2} =6 \\\ a_2= \frac{12}{6} =2 \\\ P=2(a+b) \\\ P=2\cdot(6+2)=16(sm)$
Ответ: 16см