Rectangles are one of the most basic and important shapes in geometry. They are two-dimensional figures with four straight sides and four right angles. The breadth of a rectangle is one of its defining characteristics, and is an important measurement in a variety of applications.
Definition of Breadth:
In a rectangle, the breadth is the shorter of the two sides. It is also known as the width or the shorter dimension. The other side is called the length or the longer dimension.
Calculating Breadth:
To calculate the breadth of a rectangle, you can use the formula:
breadth = area ÷ length
where area is the total area of the rectangle and length is the longer dimension.
Alternatively, you can use the formula:
breadth = perimeter ÷ 2 – length
where perimeter is the total distance around the rectangle.
Examples:
A rectangle has an area of 60 square meters and a length of 10 meters. What is its breadth?
Using the formula, breadth = area ÷ length, we get:
breadth = 60 ÷ 10 = 6 meters
Therefore, the breadth of the rectangle is 6 meters.
A rectangle has a perimeter of 24 meters and a length of 8 meters. What is its breadth?
Using the formula, breadth = perimeter ÷ 2 – length, we get:
breadth = 24 ÷ 2 – 8 = 4 meters
Therefore, the breadth of the rectangle is 4 meters.
Applications:
Knowing the breadth of a rectangle is important in a variety of fields, including construction, engineering, and design. For example, architects need to know the breadth of a room in order to design furniture that will fit comfortably within it. Builders need to know the breadth of a foundation in order to calculate the amount of materials needed for construction. Engineers need to know the breadth of a bridge in order to ensure that it can support the weight of vehicles passing over it.
Here are some sample questions and their answers related to the topic of rectangle breadth:
Q: What is the formula for finding the breadth of a rectangle? A: The formula for finding the breadth of a rectangle is: breadth = area / length, where area is the product of length and breadth.
Q: If the area of a rectangle is 60 square units and its length is 12 units, what is the breadth of the rectangle? A: Using the formula for the breadth of a rectangle, we have: breadth = area / length = 60 / 12 = 5 units. Therefore, the breadth of the rectangle is 5 units.
Q: If the length of a rectangle is twice its breadth and its perimeter is 30 cm, what are its length and breadth? A: Let the breadth of the rectangle be x. Then, the length of the rectangle is 2x. The perimeter of the rectangle is given by 2(length + breadth), which is equal to 2(2x + x) = 6x. Setting this equal to 30 cm, we have 6x = 30, or x = 5 cm. Therefore, the breadth of the rectangle is 5 cm and its length is 2x = 10 cm.
Q: If the length of a rectangle is 8 cm and its area is 48 square cm, what is its breadth? A: Using the formula for the area of a rectangle, we have: area = length x breadth. Substituting the given values, we get: 48 = 8 x breadth. Solving for breadth, we get: breadth = 48 / 8 = 6 cm. Therefore, the breadth of the rectangle is 6 cm.
The breadth of a rectangle is an important measurement that is used in a variety of applications. It is the shorter of the two sides and can be calculated using the formulas mentioned above.
