Extension Question:
Create a rectangle with dimensions of your choosing with the given parameters: the length is equal to 3 times the width. (1 point)
Find the area and perimeter of the rectangle. (2 points)
Let's say the width of the rectangle is w. Based on the given parameters, the length would be 3 times the width, so the length would be 3w.
The area of a rectangle is calculated by multiplying the length and width. Therefore, the area of this rectangle would be:
Area = Length * Width
Area = (3w)(w)
Area = 3w^2
The perimeter of a rectangle is calculated by adding up all the sides. In this case, we have two equal sides (length and width) and two equal sides (width and length). Therefore, the perimeter would be:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (3w + w)
Perimeter = 2 * 4w
Perimeter = 8w
So the area of the rectangle is 3w^2 and the perimeter is 8w.
To find the rectangle's area and perimeter, we need to determine the dimensions of the rectangle. Given that the length is equal to 3 times the width, let's choose a width of 5 units.
For a width of 5 units, the length would be 3 times that, which is 15 units.
Now that we have determined the dimensions of the rectangle, we can proceed to calculate its area and perimeter.
1. Area of the rectangle:
The area of a rectangle can be found by multiplying its length by its width.
In this case, the width is 5 units and the length is 15 units.
So, the area of the rectangle is 15 units × 5 units = 75 square units.
2. Perimeter of the rectangle:
The perimeter of a rectangle can be found by adding the lengths of all its sides.
In this case, the rectangle has two pairs of equal sides (each side is equal to the width or length).
So, the perimeter of the rectangle would be 2 × (width + length).
Substituting the given values, we get: 2 × (5 units + 15 units) = 2 × 20 units = 40 units.
Therefore, the area of the rectangle is 75 square units, and its perimeter is 40 units.
To create a rectangle with dimensions where the length is equal to 3 times the width, we can follow these steps:
Step 1: Choose a value for the width of the rectangle.
Let's say we choose a width of 5 units.
Step 2: Multiply the width by 3 to find the length.
Since the length is equal to 3 times the width, we can multiply the chosen width (5 units) by 3.
Length = Width * 3
Length = 5 units * 3
Length = 15 units
So, the rectangle has a width of 5 units and a length of 15 units.
Now, let's move on to finding the area and perimeter of the rectangle:
Area of a rectangle: The area of a rectangle is given by the formula: Area = Length * Width.
Perimeter of a rectangle: The perimeter of a rectangle is given by the formula: Perimeter = (2 * Length) + (2 * Width).
Using the dimensions we found earlier:
Area = Length * Width
Area = 15 units * 5 units
Area = 75 square units
Perimeter = (2 * Length) + (2 * Width)
Perimeter = (2 * 15 units) + (2 * 5 units)
Perimeter = 30 units + 10 units
Perimeter = 40 units
So, the area of the rectangle is 75 square units and the perimeter is 40 units.