Find the length of the sides of a rectangle

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In math class, you will learn about various geometric shapes that you can calculate. So does the simple rectangle. You can determine the side lengths of such a rectangle if you know certain other sizes.

General information about the rectangle and its side lengths

A rectangle is a body that has four edge lines, two of which are always facing each other, i.e. run parallel to each other.

  • The interior angles of a rectangle together always result in a value of 360 °, each individual angle is usually exactly 90 °, which corresponds to a right angle.
  • The sides of a rectangle are accordingly perpendicular to one another, but are not necessarily of the same length. This is only the case with a special form of the rectangle, the square.
  • A rectangle can be divided into two equal parts by a diagonal Triangles divide, whereby the diagonal then forms the hypotenuse of the triangles.

So you can easily determine the side lengths of the rectangle

  • There is the mathematical formula for the area of ​​a rectangle: A = a times b, where A stands for the area and a and b for the two sides.
    • How do I calculate the area of ​​a quadrilateral?

    If the area of ​​a quadrilateral is to be calculated, it must first be clarified ...

  • If you have now given this area and a side length, you can solve the formula for the missing size and calculate the length accordingly: a = A² / b or b = A2 / a.

Determine the lengths using the law of sines

For example, if you have the diagonal and a angle of the triangle into which the diagonal divides the rectangle, you can also determine the side length.

  1. The law of sine states that the sine of an angle is composed of its opposite cathetus divided by the hypotenuse.
  2. You can solve this formula accordingly for a side length, the opposite side: opposite side = sin alpha times hypotenuse. Insert both known sizes and calculate one side length b of the rectangle.
  3. Now you can use the Pythagorean Theorem to determine the missing second side length. This means that a² = b² + c². Here a is the hypotenuse and b is the previously calculated side length.
  4. Reshape the sentence and solve it for c: c² = a² - b² resp. c = root of (a-b).
  5. The result is the missing side length of the rectangle.
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