Answer:
B. (6√2 + 12) inches
Step-by-step explanation:
The length of the kite edge at upper left is ...
x/sin(45°) = x/(1/√2) = x√2
The length of the kite edge at upper right is ...
x/sin(30°) = x/(1/2) = 2x
The 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
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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
