Question

What is the correct answer​

Answer 1

54.64 cm

Step-by-step explanation:

The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can find the perimeter by adding all four sides of a rectangle. Perimeter of the given rectangle is a + b + a + b.

Length of CD = 17.32 cm from :

`\sin(60) = (cd)/(20) \\ then \: x = 17.32 \: cm`

now CD = BA

Now we must determine length of AD :

`\sin(30) = (ad)/(20) \: then \: ad \: = 10 \: cm`

Now :

perimeter = 17.32 + 17.32 +10+10 = 54.64 cm

Answer 2

Answer: 54.6 cm (choice B)

===================================================

Step-by-step explanation:

Focusing on triangle ACD, we see that AC = 20 is the hypotenuse and AD = 20/2 = 10 is the short leg. The short leg is half that of the hypotenuse when working with 30-60-90 triangles.

Also, for these types of triangles, the long leg is sqrt(3) times that of the short leg. That makes CD = AD*sqrt(3) = 10*sqrt(3)

The opposite sides are the same length, meaning BC = AD and AB = CD.

-----------

The perimeter of rectangle ABCD is

P = AB+BC+CD+AD

P = 10*sqrt(3) + 10 + 10*sqrt(3) + 10

P = 20 + 20*sqrt(3)

P = 54.6410161513776

P = 54.6 cm is the approximate perimeter