Step-by-step explanation:
You need to use trigonometric stuff here. Since you're given the hypotenuse and an angle you can plug that right into an equation.
Recall that sin is opposite over hypotenuse and cos is adjacent over hypotenuse.
[tex]sin(\theta)=\frac{o}{h} \\sin(30)=\frac{x}{14} \\0.5=\frac{x}{14} \\x=7[/tex]
Now that you know the opposite side (DC) you can use tan, too, but I'm going to use cos.
[tex]cos(\theta)=\frac{a}{14} \\cos(30)=\frac{x}{14} \\\frac{\sqrt{3} }{2} =\frac{x}{14} \\x=7\sqrt{3}[/tex]
This is the adjacent side (BC). I put it in its exact value, but in decimal form it's ≈12.124.
Now you can do the perimeter:
[tex]2l+2w\\2(12.124)+2(7)\\24.248+14\\38.25[/tex]
Your answer is the 38.2
