The diagonal of rectangle ABCD measures 2 inches in length. What is the length of line segment AB?
1 inch, (sqr root) 3 inches, 4 inches, (sqr root) 4/3 inches

Solution:

Given, length of the diagonal of rectangle ABCD = 2 inches.

We have to find the length of the line segment AB.

We know, opposite sides of a rectangle are equal.

Thus, AB = CD

Now consider triangle DCB, which is a right angled triangle

In triangle DCB, angle C is 90°

Angle D is 30°

Angle B is 60°

By Pythagoras theorem,

sin θ = opposite/hypotenuse

sin 60° = CD/BD

√3/2 = CD/2

CD = 2(√3/2)

CD = √3

Thus, AB = CD = √3

Therefore, the length of the line segment is √3 inches.

The diagonal of rectangle ABCD measures 2 inches in length. What is the length of line segment AB?

Summary:

The diagonal of the rectangle ABCD measures 2 inches in length. The length of line segment AB is √3 inches.