Question

The diagram shows rectangle ABCD, with diagnal BD. What is the perimeter of rectangle ABCS, to the nearest tenth?

Answer 1

Answer:

Perimeter of rectangle ABCD = 32.8 unit (Approx.)

Step-by-step explanation:

Given:

Hypotenuse BD = 12 unit

Angle θ = 30°

Find:

Perimeter of rectangle ABCD

Computation:

Using trigonometry function

Sin θ = Perpendicular / Hypotenuse

Sin 30 = CD / BD

0.5 = CD / 12

Length of CD = 6 unit

Cos θ = Base / Hypotenuse

Sin 30 = BC / BD

0.866 = BC / 12

Length of BC = 10.4 unit

Perimeter of rectangle ABCD = 2[Length + Width]

Perimeter of rectangle ABCD = 2[6 + 10.4]

Perimeter of rectangle ABCD = 2[16.4]

Perimeter of rectangle ABCD = 32.8 unit (Approx.)