Length and Width of Rectangle - Calculator
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.
P = 2 * W + 2 * L (1)
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
QuestionThe 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?
AnswerThe picture below shows the rectangle with the area of 45cm2. Now, let the width be w. Since, the length is 4cm greater than the width, the length will be w+4cm.
Before we can find the dimensions of the rectangle, we need find wfirst. Here's how:
1) Write an equation that relates 45cm2, w+4 and w.
To do so, we know that the area of the rectangle, 45cm2can be found by multiplying wwith 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 wis the width of a rectangle. There is no way it can be a negative number. Therefore, wmust be 5.
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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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?
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
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Rectangle of find dimension
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