Question

((Please Answer with A B C or D))

If x = 3 inches, what is the perimeter of the figure above?
A. (36
`√(2)` + 36) inches
B. (6
`√(2)` + 12) inches
C. 72 inches
D. (6
`√(3)` + 12) inches

Answer 1

B

Explanation:

I was told to put down A B C or D

And B was right

Answer 2

B. (6√2 + 12) inches

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

_____

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