Question

the diagonal of rectangle abcd measures 2 inches in length. what is the length of line segment ab? 1 inch √3 inches 4 inches 4√3 inches

Explanation:

Step1: Identify right - triangle properties

In right - triangle ABD of rectangle ABCD, the diagonal BD = 2 inches, and ∠ADB = 30°. In a 30 - 60 - 90 right - triangle, if the hypotenuse is \(c\), the side opposite the 30° angle is \(a=\frac{c}{2}\) and the side opposite the 60° angle is \(b = a\sqrt{3}\).

Step2: Determine the length of AB

Since AB is opposite the 30° angle in right - triangle ABD and the hypotenuse BD = 2 inches, using the 30 - 60 - 90 triangle ratio, if the hypotenuse \(c = BD=2\) inches, then the side opposite the 30° angle \(AB=\frac{BD}{2}\). So \(AB = 1\) inch.

Answer:

1 inch