Question

select the correct answer. rounded to the nearest tenth, what is the perimeter of rectangle abcd? a. 10.8 inches b. 13.7 inches c. 15.0 inches d. 18.7 inches

Explanation:

Step1: Identify right - triangle relationships

In right - triangle ADC, if the hypotenuse AC = 5 inches and one angle is 30°. Let the side opposite the 30° angle be \(x\) and the side opposite the 60° angle be \(y\). In a 30 - 60 - 90 triangle, if the hypotenuse \(c\) is given, the side opposite the 30° angle \(a=\frac{c}{2}\) and the side opposite the 60° angle \(b = \frac{\sqrt{3}}{2}c\).
So, \(AD=\frac{5}{2}=2.5\) inches and \(DC=\frac{\sqrt{3}}{2}\times5\approx\frac{1.732\times5}{2}=4.33\) inches.

Step2: Calculate the perimeter of the rectangle

The perimeter \(P\) of a rectangle \(ABCD\) is \(P = 2(AD + DC)\).
\(P=2(2.5 + 4.33)=2\times6.83 = 13.66\approx13.7\) inches.

Answer:

B. 13.7 inches