Length and Width of Rectangle Given Area Calculator

Created by Aleksandra Zając, MD
Reviewed by Vishnuvardhan Shakthibala
Last updated: Mar 14, 2022

If you're struggling to find all those unknowns surrounding rectangles, you're in the right place. Length and width of 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!

How to find the width and length of a rectangle given area and perimeter?

Let's solve it step by step.

P = perimeter,
A = area,
L = length,
W = width.

We know, that
P (perimeter) = 2L + 2W
and
A (area) = L × W

Let's determine W from the first equation.

W=P2LW=\frac{P}{2-L}

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

A=L×P2LA=L\times\frac{P}{2-L}

Which we can also express as:

L2L×P2+A=0L^2 - L\times\frac{P}{2} + A = 0

Solving the equation above, we will obtain L. Then, to find W, we can use
W = A/L or W = (P/2) - L

How to use the length and width of a rectangle given area calculator?

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 deal with it.
  4. Now, you can find both results at the very bottom of the length and width of the rectangle given area calculator.

FAQ

How to find the length of the rectangle given area and width?

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.

How to find the width of a rectangle with perimeter and length?

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

  1. Determine the equation for 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=perimeter2lentghwidth =\frac{perimeter}{2} - lentgh
  1. That way, you can quickly determine the rectangle's width with perimeter and length given.

How to determine the length and width of a rectangle given area and perimeter?

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

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

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

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

W = P/(2-L)

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

A = L × P/(2-L)
or
L2 - L × P/2 + A = 0

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

A = L × W
W = A/L

How to find the width of a rectangle given perimeter 16 in and length 5 in?

To find the width of 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 / - 10 in
6 in = 2 × W / : 2
W = 3 in
4. The answer is: width of this rectangle is three inches.

Aleksandra Zając, MD
Image of a rectangle with sides a and b, diagonal d, perimeter and area marked.
Area (A)
in²
Perimeter
in
Length (a)
in
Width (b)
in
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