Find the perimeter and area of a rectangle with a width of 2√7 - 2√5 and a length of 3√7 + 3√5

perimeter = twice width + twice length

area = length * width
= (3√7 + 3√5 )(2√7 - 2√5 )

= 6*7 + 0 - 6*5

= 12

Thank you

To find the perimeter and area of a rectangle with the given dimensions, we will use the following formulas:

1. Perimeter of a rectangle = 2 × (Length + Width)
2. Area of a rectangle = Length × Width

Let's begin by substituting the given values into the formulas:

Width = 2√7 - 2√5
Length = 3√7 + 3√5

1. Perimeter of the rectangle:
Perimeter = 2 × (Length + Width)
Substituting the values:
Perimeter = 2 × ((3√7 + 3√5) + (2√7 - 2√5))
Simplifying the expression inside the parentheses:
Perimeter = 2 × (3√7 + 2√7 + 3√5 - 2√5)
Combining like terms:
Perimeter = 2 × (5√7 + √5)
Simplifying further:
Perimeter = 10√7 + 2√5

2. Area of the rectangle:
Area = Length × Width
Substituting the values:
Area = (3√7 + 3√5) × (2√7 - 2√5)
Distributing and combining like terms using the FOIL method:
Area = 6(√7 × √7) - 6(√7 × √5) + 6(√5 × √7) - 6(√5 × √5)
Simplifying square roots:
Area = 6(7) - 6(√35) + 6(√35) - 6(5)
Simplifying further:
Area = 42 - 30
Area = 12

Therefore, the perimeter of the rectangle is 10√7 + 2√5, and the area is 12.