## Length and Width of Rectangle - Calculator

*A = L * W*

Then these equations are solved for L and W which are the length and width of the rectangle.

__How to use the calculator__

Enter the perimeter P and area A as positive real numbers and press "enter". The outputs are the width, length and diagonal of the rectangle. There are conditions under which this problem has a solution (see formulation of problem below).

__Formulation of Problem__

Let P be the perimeter of a rectangle and A its area. Let W and L be, respectively, the width and length of the rectangle. Find W and L in terms of P and A. __solution__

P = 2 * W + 2 * L (1)

and

A = W * L (2)

solve equation (1) for W:

W = P / 2 - L

and W by P / 2 - L in A = W * L to obtain

A = L * (P / 2 - L)

Rewrite as a standard quadratic equation in L

L^{ 2} - L (P / 2) + A = 0

Solve the above equation for L and find W using W = P / 2 - L.

Practice: Find the discriminant of the above quadratic equation and find the condition on P and A under which the above problem has no solution.

## Find the dimensions of a rectangle

by a visitor

**Question**

The area of a rectangle is 45 square cm. If the length is 4 cm greater than the width, what is the dimensions of the rectangle?**Answer**

The picture below shows the rectangle with the area of 45cm^{2}. Now, let the width be

**w**. Since, the length is 4cm greater than the width, the length will be

**w+4**cm.

Before we can find the dimensions of the rectangle, we need find

**w**first. Here's how:

**1) Write an equation that relates**

*45cm*.^{2}, w+4 and wTo do so, we know that the area of the rectangle, 45cm

^{2}can be found by multiplying

**w**with

**w+4**. Hence, we have:

To continue, we need to remove the bracket and simplify the equation. This is shown below:

**2) Solve the Quadratic Equation**

Notice that, now we have a quadratic equation:

To find

**w**, we need to solve the quadratic equation. One way to do so is to factorize the quadratic equation. Hence, we have:

Now, since

**w**is the width of a rectangle. There is no way it can be a negative number. Therefore,

**w**must be 5. With

**w**= 5. The...

...and the... Below is the rectangle with its dimensions:

## 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.

Want to find complex math solutions within seconds?

Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps.

Book a Free Trial Class

**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 = l^{2} + 8

l^{2} - 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

I am not excited by this Caucasian, but by the way he observes. I discovered a secret desire in myself, if they watch me, I get even more excited by it. I cling tightly to my new acquaintance. I begin to rip off his shirt, then rip the strap off his trousers and pull his trousers down.

## Rectangle of find dimension

The unhappy woman stood with her back to me. Apparently she was embarrassed to undress in front of me. She untied the belt, then slowly bent down, took the hem of the dress and, writhing slightly, began to pull off the fabric that. Tightly hugged her seductive figure.

Find Rectangle Dimensions with Given Perimeter and AreaNow everything has become simple: Almost all of them were not widows, strictly speaking, but straw widows. "Yeah, yeah, your beloved has disappeared without a trace. " It somehow didnt work out in a human way.

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