Rounded to the nearest tenth, what is the perimeter of rectangle ABCD? rectangle ABCD with diagonal AC, labeled as measuring 20 centimeters, angle BAC measuring 30 degrees, angle BCA measuring 60 degrees, angle DCA measuring 30 degrees, and angle DAC measuring 60 degrees A. 48.3 cm B. 54.6 cm C. 60.0 cm D. 173.2 cm

54.6 cm : B

Step-by-step explanation:

Mathematically the area of a rectangle is 2( l + b)

So in practical terms we only need the measure of two sides as we have 2 equal sides for a rectangle.

We can see that we have two right angles on each sides

Now to find b, we can use trigonometric ratios

For each of the rectangles, the diagonal represents the hypotenuse

Mathematically;

sin 30 = b/20

From triangle ABC

b = 20 sin 30 = 20 * 0.5 = 10 cm

Now, to get l

Mathematically;

Sin 60 = l/20

l = 20 sin 60 = 17.32 cm

So the perimeter is;

2(10 + 17.32)

2(27.32) = 54.64 cm which is 54.6 to the nearest tenth