In the space below find the perimeter and area of the rectangle with the following dimensions:
Length=×+7
Width=3×-1
To find the perimeter of a rectangle, you add up all the sides of the rectangle.
Perimeter = 2(Length + Width)
Given:
Length = × + 7
Width = 3× - 1
Let's substitute these values into the perimeter formula:
Perimeter = 2((× + 7) + (3× - 1))
Expand the brackets:
Perimeter = 2(× + 7 + 3× - 1)
Simplify:
Perimeter = 2(4× + 6)
Multiply:
Perimeter = 8× + 12
Therefore, the perimeter of the rectangle is 8× + 12.
To find the area of a rectangle, you multiply the length by the width.
Area = Length x Width
Given:
Length = × + 7
Width = 3× - 1
Let's substitute these values into the area formula:
Area = (× + 7)(3× - 1)
Expand the brackets:
Area = 3×^2 - × + 21× - 7
Combine like terms:
Area = 3×^2 + 20× - 7
Therefore, the area of the rectangle is 3×^2 + 20× - 7.