Diagonal of Rectangle

While learning how to find out the area and perimeter of a rectangle, we came across the term diagonal many a times. In this article, we will learn about the diagonal and how to calculate it.

What is the Diagonal of a Rectangle

The diagonal of a rectangle is the line segments linking opposite vertices or corners of the rectangle.

A rectangle has two diagonals. Each diagonal is a line segment connecting the opposite vertices of a rectangle.

Properties

1. The 2 diagonals are congruent (equal in length);  here AC and BD are the diagonals & AC = BD
2. The diagonals bisect each other equally; here AC & BD bisect each other
3. Each diagonal divides a rectangle into 2 congruent right-angled triangles; here AC divides ▭ ABCD into 2 ∆ABC and ∆ADC;  BD divides ▭ ABCD into ∆BCD and ∆BAD
4. The diagonals are not perpendicular to each other; here diagonals AC & BD are not perpendicular
5. The adjacent central angles at the point of intersection are not equal, but the opposite central angles are equal; here ∠AOB = ∠COD & ∠BOC = ∠AOD, but ∠AOB  ≠ ∠AOD or ∠BOC, & ∠BOC ≠ ∠COD or ∠AOB

Formula

The formula to find the diagonal of a rectangle is given below:

Derivation

Applying Pythagorean theorem in ▭ ABCD, we get,

=> d² = w² + l² , here d = diagonal, l = length, w = width

Taking square root on both sides,

d = √(w² + l²)

Thus we get the formula to calculate the diagonal of a rectangle.

Let us see how to calculate the diagonals of rectangles by solving some examples.

Solved Examples

FAQs