Answer:
20 cm.
Step-by-step explanation:
We know that the permiter is defined as
[tex]P=L+S+M[/tex]
Where [tex]L[/tex] is the longest side, [tex]S[/tex] is the smallest and [tex]M[/tex] is the middle side.
If [tex]L=x[/tex] then, [tex]S=x-20[/tex], where we need to find an expression for [tex]M[/tex] using the law of cosines.
[tex]M^{2} =L^{2}+S^{2}-2 \times L \times S \times cos(60\°)\\M=\sqrt{x^{2}+(x-20)^{2}-x(x-20)}\\M=\sqrt{x^{2} +x^{2}-40x+400-x^{2}+20x}=\sqrt{x^{2}-20x+400}[/tex]
Replacing all expression, the perimeter is
[tex]P=x+x-20+\sqrt{x^{2}-20x+400}\\P=2x-20+\sqrt{x^{2}-20x+400}[/tex]
Using a calculator, the perimeter is 20 units centimeters.
