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Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length Formula

GoPerimeter of Rectangle Formula

GoPerimeter of Rectangle given Diagonal and Length Formula

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Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle. Check FAQs

P = 2 \cdot d \cdot \sqrt{1 + (2 \cdot \sin (∠ dl) \cdot \cos (∠ dl))}

P - Perimeter of Rectangle?d - Diagonal of Rectangle?∠_dl - Angle between Diagonal and Length of Rectangle?

Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length Example

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Here is how the Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length equation looks like with Values.

Here is how the Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length equation looks like with Units.

Here is how the Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length equation looks like.

27.8546 = 2 \cdot 10 \cdot \sqrt{1 + (2 \cdot \sin (35) \cdot \cos (35))}

27.8546m = 2 \cdot 10m \cdot \sqrt{1 + (2 \cdot \sin (35°) \cdot \cos (35°))}

27.8546 = 2 \cdot 10 \cdot \sqrt{1 + (2 \cdot \sin (35) \cdot \cos (35))}

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Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length Solution

Follow our step by step solution on how to calculate Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length?

FIRST Step Consider the formula

P = 2 \cdot d \cdot \sqrt{1 + (2 \cdot \sin (∠ dl) \cdot \cos (∠ dl))}

Next Step Substitute values of Variables

∴

P = 2 \cdot 10m \cdot \sqrt{1 + (2 \cdot \sin (35°) \cdot \cos (35°))}

Next Step Convert Units

∴

P = 2 \cdot 10m \cdot \sqrt{1 + (2 \cdot \sin (0.6109rad) \cdot \cos (0.6109rad))}

Next Step Prepare to Evaluate

∴

P = 2 \cdot 10 \cdot \sqrt{1 + (2 \cdot \sin (0.6109) \cdot \cos (0.6109))}

Next Step Evaluate

∴

P = 27.8545696128002m

LAST Step Rounding Answer

∴

P = 27.8546m

Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length Formula Elements

Variables

Functions

Perimeter of Rectangle

Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.

Symbol: P

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Perimeter of Rectangle

Diagonal of Rectangle

Diagonal of Rectangle is the length of the line joining any pair of opposite vertices of the Rectangle.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal of Rectangle

Angle between Diagonal and Length of Rectangle

Angle between Diagonal and Length of Rectangle is the measure of wideness of the angle made by any diagonal with the length of the Rectangle.

Symbol: ∠_dl

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Angle between Diagonal and Length of Rectangle

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Perimeter of Rectangle

Go Perimeter of Rectangle

P = 2 \cdot (l + b)

Go Perimeter of Rectangle given Diagonal and Length

P = 2 \cdot (l + \sqrt{d^{2} - l^{2}})

Go Perimeter of Rectangle given Area and Length

P = \frac{2 \cdot (A + l^{2})}{l}

Go Perimeter of Rectangle given Breadth and Circumradius

P = 2 \cdot (b + \sqrt{(4 \cdot {r c}^{2}) - b^{2}})

How to Evaluate Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length?

Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length evaluator uses Perimeter of Rectangle = 2*Diagonal of Rectangle*sqrt(1+(2*sin(Angle between Diagonal and Length of Rectangle)*cos(Angle between Diagonal and Length of Rectangle))) to evaluate the Perimeter of Rectangle, The Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length formula is defined as the total length of all the boundary lines of the Rectangle, and calculated using Diagonal and Angle between Diagonal and Length of the Rectangle. Perimeter of Rectangle is denoted by P symbol.

How to evaluate Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length using this online evaluator? To use this online evaluator for Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length, enter Diagonal of Rectangle (d) & Angle between Diagonal and Length of Rectangle (∠_dl) and hit the calculate button.

FAQs on Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length

What is the formula to find Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length?

The formula of Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length is expressed as Perimeter of Rectangle = 2*Diagonal of Rectangle*sqrt(1+(2*sin(Angle between Diagonal and Length of Rectangle)*cos(Angle between Diagonal and Length of Rectangle))). Here is an example- 27.85457 = 2*10*sqrt(1+(2*sin(0.610865238197901)*cos(0.610865238197901))).

How to calculate Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length?

With Diagonal of Rectangle (d) & Angle between Diagonal and Length of Rectangle (∠_dl) we can find Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length using the formula - Perimeter of Rectangle = 2*Diagonal of Rectangle*sqrt(1+(2*sin(Angle between Diagonal and Length of Rectangle)*cos(Angle between Diagonal and Length of Rectangle))). This formula also uses SineCosine, Square Root Function function(s).

What are the other ways to Calculate Perimeter of Rectangle?

Here are the different ways to Calculate Perimeter of Rectangle-

Perimeter of Rectangle=2*(Length of Rectangle+Breadth of Rectangle)
Perimeter of Rectangle=2*(Length of Rectangle+sqrt(Diagonal of Rectangle^2-Length of Rectangle^2))
Perimeter of Rectangle=(2*(Area of Rectangle+Length of Rectangle^2))/Length of Rectangle

Can the Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length be negative?

No, the Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length, measured in Length cannot be negative.

Which unit is used to measure Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length?

Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length can be measured.

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