Diagonals in a Rectangle

A rectangle is a four-sided polygon with opposite sides that are equal in length and four right angles. Diagonals are line segments that connect two nonadjacent vertices of a polygon. In the case of a rectangle, the diagonals connect the opposite corners or vertices of the rectangle.

Calculating the Number of Diagonals

To determine the number of diagonals in a rectangle, we need to consider the number of possible pairs of nonadjacent vertices. In a rectangle, there are two pairs of opposite vertices. Let's examine each pair separately.

1. Pair of Opposite Vertices on the Longer Side:
- The longer side of a rectangle is also known as its length.
- Let's assume the length of the rectangle is 'L'.
- The longer side has two opposite vertices.
- These two vertices can be connected by a diagonal.
- Therefore, there is 1 diagonal formed by this pair of vertices.

2. Pair of Opposite Vertices on the Shorter Side:
- The shorter side of a rectangle is also known as its width.
- Let's assume the width of the rectangle is 'W'.
- The shorter side has two opposite vertices.
- These two vertices can also be connected by a diagonal.
- Therefore, there is 1 diagonal formed by this pair of vertices.

Total Number of Diagonals

By adding up the number of diagonals formed by each pair of opposite vertices, we can determine the total number of diagonals in a rectangle.

In this case, we have:
- 1 diagonal formed by the pair of opposite vertices on the longer side.
- 1 diagonal formed by the pair of opposite vertices on the shorter side.

Therefore, a rectangle has a total of 2 diagonals.

Conclusion

To summarize, a rectangle has two diagonals. One diagonal is formed by a pair of opposite vertices on the longer side, while the other diagonal is formed by a pair of opposite vertices on the shorter side.