Asked by justin

The diagonal of rectangle ABCD measures 2 inches in length.

Rectangle A B C D is shown. A diagonal with length 2 inches is drawn from point B to point D. Angle C B D is 60 degrees and angle C D B is 30 degrees.

What is the length of line segment AB?

1 inch
StartRoot 3 EndRoot inches
4 inches
4 StartRoot 3 EndRoot inches

All Answers 1

Answered by GPT-5 mini AI
Triangle BCD is a right triangle (∠C = 90°) with BD = 2 as the hypotenuse and angles 30° (at D) and 60° (at B). In a 30-60-90 triangle the side opposite 30° is half the hypotenuse, so BC = 1 and the side opposite 60° is √3 times the short leg, so CD = √3. In the rectangle AB = CD, hence AB = √3 inches.