Length and Width of a Rectangle Given Area Calculator

You're in the right place if you're struggling to find all those unknowns surrounding rectangles. Length and width of a rectangle given area calculator will answer at least part of your questions. You should provide the area and perimeter. Read on to dig deeper into the topic and learn how to find the length and width of a rectangle given area even without a calculator!

Let's solve it step by step.

P = perimeter;
A = area;
L = length; and
W = width.

We know that;

P (perimeter) = 2L + 2W

and:

A (area) = L × W

Let's determine W from the first equation.

And now let's use that in the second equation:

Which we can also express as:

Solving the equation above, we will obtain L. Then, to find W, we can use:

W = A/L or W = (P/2) - L

To determine the length and width of a rectangle, you need to:

1. Know the area of the rectangle.
2. Know the perimeter of the rectangle.
3. Type the area and perimeter values into the calculator. Don't worry if they come in different units - the calculator will do the length conversion.
4. Now, you can find both results at the very bottom of the length and width of the rectangle given area calculator.

Have you still got questions after using this length and width of a rectangle given area calculator? Check out the rest of our rectangle-related tools:

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To find the length (L) of a rectangle given area (A) and width (W), you need to:

1. Know the equation for a rectangle area is A = L × W.
2. Determine L from that previous equation. L = A/Q.

To sum up: to find the length of a rectangle, you need to divide its area by the known width.

To find the width of a rectangle with a known perimeter and length:

1. Determine the equation for the perimeter:

   Perimeter (P) = 2 × length (L) + 2 × width (W)

2. Transform the equation:

   P - 2 × L = 2 × W
P/2 - L = W

   so that your final formula is:

   width = perimeter / 2 - length

3. That way, you can quickly determine the rectangle's width with the perimeter and length given.

To determine the length and width of a rectangle given area and perimeter:

1. State the equations for both area (A) and perimeter (P).

   A = length (L) × width (W)
   P = 2L + 2W

2. From the first equation, we can also express W as:

   W = P/(2-L)

3. Putting this into the second equation will look like this:

   A = L × P/(2-L),

   or:

   L² - L × P/2 + A = 0

4. Solving this equation, we will know L - length. Then we can easily determine width as well, knowing that:

   A = L × W
   W = A/L

To find the width of a rectangle given perimeter (16 in) and length (5 in):

1. Determine the equation for perimeter:

   P(perimeter) = 2 × L (length) + 2 × W (width)

2. As we already know the perimeter and length, we can rewrite the equation:

   16 in = 2 × 5 in + 2 × W

3. Let's solve this equation:

   16 in = 10 in + 2 × W
6 in = 2 × W
W = 3 in

4. The answer is: width of this rectangle is three inches.