Create a rectangle with dimensions of your choosing with the given parameters: the length is equal to √3 times the width.
Find the area of the rectangle.
Let's assume the width of the rectangle is "x".
According to the given parameters, the length of the rectangle is √3 times the width, so it would be (√3)x.
The area of a rectangle is calculated by multiplying the length and width. Therefore, the formula for calculating the area (A) of the rectangle is:
A = length × width
Substituting the given values into the formula:
A = (√3)x × x
A = √3x^2
So, the area of the rectangle is √3x^2.
To create a rectangle with dimensions that satisfy the given parameters, we first need to find the relationship between the length and the width.
Let's assume the width of the rectangle is denoted as "w". According to the given parameters, the length of the rectangle is equal to √3 times the width. Mathematically, this can be expressed as:
Length = √3 * Width
Now, let's calculate the length in terms of the width:
Length = √3 * w
To find the area of the rectangle, we need to multiply the length by the width:
Area = Length * Width
Substituting the value of the length from the equation above:
Area = (√3 * w) * w
Area = √3w^2
Therefore, the area of the rectangle, in terms of the width, is √3w^2.
To create a rectangle with length (√3 * width), we need to assign a value to the width. Let's say we choose the width to be 'w'.
According to the given parameters, the length (√3 * width) would be (√3 * w).
So, the dimensions of the rectangle would be:
Length = (√3 * w)
Width = w
To find the area of a rectangle, we need to multiply the length and width.
Area of the rectangle = Length * Width
Substituting the values:
Area = (√3 * w) * w
Area = √3w^2
Thus, the area of the rectangle is √3 times the square of the width (√3w^2).