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: Recall right - triangle properties

In rectangle \(ABCD\), \(\angle A = 90^{\circ}\), and the diagonal \(BD = 2\) inches. If we assume \(\angle ADB=30^{\circ}\), in a right - triangle (\(\triangle ABD\)), we can use trigonometric relations or the 30 - 60 - 90 triangle ratio. The ratio of the sides in a 30 - 60 - 90 triangle is \(1:\sqrt{3}:2\) (where the side opposite the \(30^{\circ}\) angle is the shortest, the side opposite the \(60^{\circ}\) angle is \(\sqrt{3}\) times the shortest side, and the hypotenuse is 2 times the shortest side).

Step2: Identify the side length

The diagonal \(BD\) is the hypotenuse of right - triangle \(\triangle ABD\). Side \(AB\) is opposite the \(30^{\circ}\) angle. According to the 30 - 60 - 90 triangle ratio, if the hypotenuse \(BD = 2\) inches, then the side opposite the \(30^{\circ}\) angle (\(AB\)) is 1 inch.

Answer:

1 inch