Rectangle Length Formula with Solved Examples
A rectangle could even be a closed 2-D shape, having four sides, four corners, and 4 proper angles [90°]. The rectangles are equal and parallel. Since a rectangle is a 2-D shape, it's characterized by two dimensions, length, and width. Length is the longer aspect of the rectangle and width is that of the shorter side. Examples of Rectangle:
Parks and Agriculture lands
Canvas
Tiles
Tables, etc.
Rectangle
Length and Breadth of Rectangle:
We know that a rectangle is a Polygon shape in which the opposite sides are parallel and equal to each other and all four angles are right angles.
The longer side of the rectangle is known as the length of the rectangle.
The shorter side of the rectangle is known as the breadth of the rectangle. Breadth is additionally referred to as the width of a rectangle.
Breadth of the Rectangle
What are Length and Breadth:
Length - The definition of length is the measurement or extent of anything from beginning to conclusion. To put it another way, it is the greater of the higher two or three dimensions of a geometric form or object. A rectangle, for instance, has length and breadth as its dimensions. Additionally, the length might be a quantity in the International System of Quantities with the dimension distance.
Breadth - A similar word to width is breadth. A thing's breadth is the distance between its facets and features. Often, this is a noun. When a verbal desire is categorical regarding an object's size, the term is employed. For instance, when someone asks about the width of something, they are actually referring to the measurement. Additionally, it can be utilized to capture a range or variation of something that cannot be quantified. This might be a special talent or area of knowledge that a person possesses.
Length of Rectangle Formula:
If we've area of a rectangle is A; the breadth of a rectangle is B and the length of the rectangle is going to be L; so
Length formula:
\[{\rm{L = }}\dfrac{{\rm{A}}}{{\rm{B}}}\]
Length \[ = \] Area \[ \div \] Breadth
If we've perimeter of a rectangle is P, the breadth of the rectangle be B, and the length of the rectangle will be L; so
Length formula:
\[{\rm{L}} = \dfrac{{\rm{P}}}{2} - {\rm{B}}\]
Length = Perimeter ÷2 – Breadth
Breath of Rectangle Formula:
If we've area of a rectangle is A; the length of the rectangle be L and the breadth of the rectangle is going to be B; so
\[{\rm{B = }}\dfrac{{\rm{A}}}{{\rm{L}}}\]
Breadth \[ = \] Area \[ \div \] Length
If we've Perimeter of the rectangle is P; the length of the rectangle is L and the breadth of the rectangle is going to be B; so
\[{\rm{B}} = \dfrac{{\rm{P}}}{2} - {\rm{L}}\]
[Breadth = Perimeter ÷2 – Length]
How to Find Length and Breadth:
Find length and breadth when the area is given
Let’s discuss how to discover size or breadth when the vicinity of a rectangle is given.
Once we would like to locate the size of a rectangle we want to divide the place via breadth.
Length of a rectangle = Area ÷ breadth
l A b
Similarly, once we would like to discover the breadth of a rectangle we want to divide the region by way of length.
The breadth of a rectangle = Area ÷ length
b A l
Find length and breadth when the perimeter is given:
Let’s discuss the thanks to finding length or breadth when the perimeter of the Rectangle is given,
When we'd wish to find the length of a rectangle we need to subtract the breadth from the perimeter by 2
Length Perimeter 2breadth
Similarly, then we'd wish to find the breadth of the rectangle. We need to subtract land from the perimeter divided by two.
Breadth Perimeter 2length
Solved Examples
1. Find the length of the opposite side of the rectangle, the given area, and one of its sides. Rectangle area \[ = \]1575 sq m side 45m
Solution: Area of the rectangle=length× breadth\[ = \]1575sq.m
One side\[ = \]45m
1575\[ = \]length\[ \times \]45.
length \[ = \frac{{1575}}{{45}} = 35\]m
The length of his visit is 35m.
2. Find the breadth of the rectangle whose perimeter is 360 cm and whose breadth is 80 cm.
Solution: Perimeter of Rectangle=360cm
Breadth \[ = \] 80cm
Length \[ = \] Perimeter/2-breadth
\[ = \]\[\frac{{360}}{2} - 80\]
\[ = 180 - 80\]
\[ = 100\]cm
Lengths are 100cm.
3. Find the length of a rectangle whose perimeter is 20 cm and breadth is 1 cm.
Solution: Perimeter of Rectangle \[ = \]20cm
Breadth \[ = \]1cm
Length\[ = \]?
Length \[ = \]perimeter/2\[ - \]breadth
\[ = \frac{{20}}{2} - 1\]
\[ = 10 - 1\]
\[ = \]9cm.
The length goes to be 9cm.
Summary
The rectangle is a quadrilateral that has 4 sides and 4 angles. The longer side of the rectangle is known as size and the Shorter side of the rectangle is referred to as Breadth. A rectangle is four-sided and all the internal angles are equal to 90 degrees. The length of the opposite sides of the rectangle is always equal to each other. If all the sides are equal then it is square.
FAQs on How to Find the Length of a Rectangle Easily
1. What are the main formulas to find the length of a rectangle?
You can find the length (L) of a rectangle using three primary formulas, depending on the information you have:
Given Area (A) and Width (W): L = A / W
Given Perimeter (P) and Width (W): L = (P / 2) - W
Given Diagonal (D) and Width (W): L = √(D² - W²)
2. How can you find the length of a rectangle if you know its area and width?
To find the length of a rectangle when you know the area and the width, you simply rearrange the area formula. The formula is Length = Area ÷ Width. For example, if a rectangle has an area of 30 square cm and a width of 5 cm, its length would be 30 ÷ 5 = 6 cm.
3. How do you calculate the length of a rectangle using its perimeter and width?
When the perimeter and width are known, you can find the length by using the formula: Length = (Perimeter / 2) - Width. This works because the perimeter is the total of two lengths and two widths. Dividing the perimeter by two gives you the sum of one length and one width. Subtracting the width then leaves you with the length.
4. Why is a square considered a special type of rectangle?
A square is considered a special type of rectangle because it fulfils all the essential properties of a rectangle. A rectangle is defined as a quadrilateral with four right angles and opposite sides that are equal in length. A square has four right angles and its opposite sides are equal. The only additional property of a square is that all four of its sides are equal, making it a more specific, or special, version of a rectangle.
5. What key properties of a rectangle are important for finding its dimensions?
The most important properties for calculations are:
Opposite sides are equal and parallel: This is the fundamental reason why formulas for perimeter and area work consistently. Knowing one length means you know the opposite side's length too.
All internal angles are 90 degrees: This property is crucial as it allows us to use the Pythagorean theorem when the diagonal is involved, treating the length, width, and diagonal as a right-angled triangle.
6. Can you find the length of a rectangle if you only know its area? Why or why not?
No, you cannot find the exact length of a rectangle if you only know its area. This is because the same area can be achieved with multiple combinations of length and width. For instance, an area of 24 square units could belong to a rectangle that is 6 units long and 4 units wide, or 8 units long and 3 units wide, or even 12 units long and 2 units wide. You need at least one other piece of information, like the width or the perimeter, to determine a unique length.
7. How is the Pythagorean theorem used to find the length of a rectangle?
The Pythagorean theorem can be used when you know the diagonal and the width of a rectangle. The diagonal, length, and width of a rectangle form a right-angled triangle, with the diagonal as the hypotenuse. According to the theorem (a² + b² = c²), we have (Length)² + (Width)² = (Diagonal)². To find the length, we rearrange this to get the formula: Length = √(Diagonal² - Width²).
8. In what real-world situations is it useful to calculate the length of a rectangle?
Calculating the length of a rectangle has many practical applications in daily life. For example:
Home Improvement: To determine the amount of flooring, carpet, or wallpaper needed for a room when you know the total area and one side.
Gardening: To plan the layout of a garden bed or calculate the length of a fence required for one side if you know the total perimeter and width.
Construction and Design: For ensuring that components like windows, doors, or foundations fit into a pre-defined area with a known width.
9. What is the key difference between the length and the perimeter of a rectangle?
The key difference lies in what they measure. Length is a one-dimensional measurement that represents the distance of one of the longer sides of the rectangle. In contrast, the perimeter is the total distance around the entire boundary of the shape. It is a cumulative measure, calculated by adding all four sides together (Perimeter = 2 x (Length + Width)).
