What will be the perimeter of a rectangle if its length is 3 times its width the length of diagonal is 8 and 10 cm?

Our diagonal of a rectangle calculator is an extensive tool that quickly finds the diagonal and other parameters of a rectangle. Have you met a specific rectangle problem and you don't know how to find the diagonal of a rectangle? Try entering a couple of parameters in the fields beside the text or keep reading to find out what are the possible diagonal of a rectangle formulas.

You can see a typical rectangle in the figure below. We have marked five basic quantities that describe a specific rectangle. You can use them to derive the diagonal of a rectangle formula. These are:

• l - length;
• w - width;
• α - the angle between diagonals;
• r - circumcircle radius;
• d - diagonal;

and two other parameters which are not shown in the picture:

• A - area; and
• P - perimeter.

The term rectangle comes from the Latin rectangulus, which is a combination of two words: rectus (right, proper) and angulus (angle). This name derives from the fact that a rectangle is a quadrilateral with four right angles (4 * 90° = 360°). Its opposite sides are parallel and of equal length, and its two diagonals intersect each other in the middle and are of equal lengths too.

A square is a special case of a rectangle. Its definition is that it has all four sides of equal length; alternatively, the angle between two diagonals is right. Try our calculators dedicated to squares, e.g., the square calc. They can quickly estimate the perimeter, area, and diagonal of every square you want, just from the length of its side.

The center of a rectangle is equidistant from its vertices; therefore, you can always circumscribe a circle on it. On the other hand, you can inscribe a circle into a rectangle only if it is a square.

To find the diagonal of a rectangle formula, you can divide a rectangle into two congruent right triangles, i.e., triangles with one angle of 90°. Each triangle will have sides of length l and w and a hypotenuse of length d. You can use the hypotenuse formula, e.g., from the Pythagorean theorem calculator, to estimate the diagonal of a rectangle, which can be expressed with the following formula:

d² = l² + w²,

and now you should know how to find the diagonal of a rectangle explicit formula - just take a square root:

d = √(l² + w²).

Our diagonal of a rectangle calculator allows you to use almost any units you want. Check out our length converter or area converter to find out how to switch between different units (SI and imperial).

Sometimes you won't have given all of two rectangle's sides. How to find the diagonal of a rectangle in that situation? The answer is provided with our diagonal of a rectangle calculator. At first, let's write down three basic equations for the area, perimeter] and circumcircle radius:

1. Area of a rectangle: A = w × l,
2. Perimeter of a rectangle P = 2 × w + 2 × l,
3. Circumcircle radius of a rectangle r = d/2.

With the above equations, we can now derive various diagonal of a rectangle formulas that are used by this diagonal of a rectangle calculator:

1. Given length and width: d = √(l² + w²);
2. Given length/width and area: d = √(A²/l² + l²) or d = √(A²/w² + w²);
3. Given length/width and perimeter: d = √(2l² - P×l + P²/4)) or d = √(2w² - P×w + P²/4);
4. Given length/width and angle: d = w / sin(α/2) or d = l / cos(α/2);
5. Given area and perimeter: d = √(P² - 2×A);
6. Given area and angle: d = √(2 × A / sin(α));
7. Given perimeter and angle: d = P / (2×sin(α/2) + 2×cos(α/2)); and
8. Given circumcircle radius: d = 2 × r.

Note: The angle α between diagonals is in the front of the length like in the first figure. Also, remember that the diagonal of a rectangle calculator assumes that the length is longer than the width!

Did you know that there is a special rectangle called the golden rectangle? If not, head on to our golden rectangle calculator to learn how you can construct golden rectangles!

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Given the rectangle in the diagram, what is the perimeter of the rectangle?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a rectangle is found by adding up the length of all four sides. Since the two long sides are 12 cm, and the two shorter sides are 7 cm the perimeter can be found by:

The perimeter is 38 cm.

One side of a rectangle is 7 inches and another is 9 inches.  What is the perimeter of the rectangle in inches?

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width).  Multiply both the height and width by two and add the results.

A rectangle has an area of

Possible Answers:

Correct answer:

Explanation:

For a rectangle, area is 

Let

The area equation to solve becomes

To factor, find two numbers the sum to -4 and multiply to -96.  -12 and 8 will work:

x2 + 8x - 12x - 96 = 0

x(x + 8) - 12(x + 8) = 0

(x - 12)(x + 8) = 0

Set each factor equal to zero and solve:

Therefore the length is 

A rancher wants to surround his rectangular field with barbed wire fence that costs $1.75 per foot. The field measures 200 yards by 400 yards. How much will the fence cost?

Possible Answers:

Correct answer:

Explanation:

Convert the dimensions from yards to feet by multiplying by 3: This makes the dimensions 600 feet and 1,200 feet. The perimeter of this farm is therefore

Multiply this by the cost of the fence per foot:

A rectangle has a length of

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of any rectangle, add all of the sides up:

20 + 20 + 12 + 12 = 64 inches

You could use this formula as well:

This formula comes from the fact that there are 2 lengths and 2 widths in every rectangle.

Find the perimeter of this rectangle.

Possible Answers:

Correct answer:

Explanation:

Remember, the perimeter of the rectangle is the sum of all four sides:

It is obvious from the figure that A=6 and B=24.

A rectangle has an area of 56 square feet, and a width of 4 feet. What is the perimeter, in feet, of the rectangle?

Possible Answers:

Correct answer: 36

Explanation:

Divide the area of the rectangle by the width in order to find the length of 14 feet. The perimeter is the sum of the side lengths, which in this case is 14 feet + 4 feet +14 feet + 4 feet, or 36 feet.

The area of a rectangle is

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is the width times the height, and we are told that in this rectangle the width is two times the height.

Therefore,

Plug in the value of the area:

Solve for 

Robert is designing a rectangular garden. He wants the area of the garden to be 9 square meters. If the length of the lot is going to be three meters less than twice the width, what will the perimeter of the lot be in meters?

Possible Answers:

Explanation:

Let l be the length of the garden and w be the width. 

By the specifications of the problem, l = 2w-3.

Plug this in for length in the area formula:

A = l  x w = (2w - 3) x w = 9

Solve for the width:

2w²- 3w - 9 =0 

(2w + 3)(w - 3) = 0

w is either 3 or -3/2, but we can't have a negative width, so w = 3.

If w = 3, then length = 2(3) - 3 = 3.

Now plug the width and length into the formula for perimeter:

P = 2 l + 2w = 2(3) + 2(3) = 12

Find the perimeter of a rectangle that has a length of 

Possible Answers:

Correct answer:

Explanation:

Recall how to find the perimeter of a rectangle:

For the given rectangle,

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