((Please Answer with A B C or D))If x = 3 inches, what is the perimeter of the figure above? A. (36[tex]\sqrt{2}[/tex] + 36) inches B. (6[tex]\sqrt{2}[/tex] + 12) inches C. 72 inches D. (6[tex]\sqrt{3}[/tex] + 12) inches

Answer:   B. (6√2 + 12) inchesStep-by-step explanation:The length of the kite edge at upper left is ...   x/sin(45°) = x/(1/√2) = x√2The length of the kite edge at upper right is ...   x/sin(30°) = x/(1/2) = 2xThe perimeter of the kite is double the sum of the lengths of these edges:   P = 2(x√2 +2x) = 2x(√2 +2)For x=3 in, this is ...   P = 2·(3 in)(√2 +2)   P = (6√2 +12) in_____The sine of an angle is the ratio of the side opposite to the hypotenuse. Here, the side opposite is x, and the hypotenuse is the kite edge of interest.   x/hypotenuse = sin(angle)   hypotenuse = x/sin(angle) . . . . . solve for hypotenuse