how to find the length

Length and Width of a Rectangle Calculator

Length and Width of a Rectangle Calculator is a free online tool which helps to find side length of rectangle.

What Is Length and Width of a Rectangle Calculator?

A rectangle is a closed two-dimensional figure with four sides and four corners. The length of the opposite sides is equal and parallel to each other.Cuemath's Length and Width of a Rectangle Calculator is a free online tool that calculates the length and the width of a rectangle within a few seconds.

Note: Enter numbers upto 3 digits.

How to Use the Length and Width of a Rectangle Calculator?

Follow the steps mentioned below to find the length and width of a rectangle.

Step 1: Enter the value of the area and perimeter of the rectangle in the respective input boxes.
Step 2: Click on "Calculate" to find the respective length and the width of the rectangle.
Step 3: Click on "Reset" to clear the fields and enter the new values.

How to Calculate Length and Width of a Rectangle?

The formula for the area, 'A' of a rectangle whose length and width are 'l' and 'w' respectively is the product of length and width, that is, "A = l × w".

The formula for the perimeter, 'P' of a rectangle whose length and width are 'l' and 'w' respectively is P = 2(l + w).

To calculate the length and width of a rectangle first, calculate the value of width 'w' by using the area of rectangle formula that is, 'w = A/l'. Then substitute the value of width in the formula of the perimeter of a rectangle and simplify the value of length 'l', that is,

P = 2 (l + A/I).

Then substitute the value of the length 'l' of the rectangle in the equation w = A/l and simplify to find the width 'w'.

Let's learn through an example how to find the length and width of a rectangle.

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Solved Example:

If the area and the perimeter of a rectangle are 8 square units and 12 units respectively. What is the length and width of the rectangle?

Solution:

Substitute the values of Area in the formula 'A = l × w' and simplify to find width 'w' in the form of length 'l'.

A = l × w
8 = l × w
w = 8/l

Substitute the value of width in the formula of the perimeter of a rectangle and simplify the value of length 'l', that is, P = 2 (l + A/I).

P = 2 (l + w)
12 = 2 (l + 8/l)
6l = l² + 8
l² - 6l + 8 = 0
l = 4 units (or) 2 units.

Substitute the value of the length 'l' of the rectangle in the equation w = A/l and simplify to find the width 'w'.

w = A/l
If l = 4 units, then w = 8/4 = 2 units.
If l = 2 units, then w = 8/2 = 4 units.

Therefore, l = 4 units (or) 2 units
w = 2 units (or) 4 units
Now, use our online length and width of a rctangle calculator and find the length and width of a rectangle if its area and perimeter are as follows:

Area = 80 square units, Perimeter = 36 units
Area = 72 square units, Perimeter = 40 units