Final answer:
To find the perimeter of the rectangle with an area of 600 m² and a length six times its width, we first find the width to be 10 m. We then calculate the length to be 60 m. Using the formula for the perimeter of a rectangle, we conclude the perimeter is 140 m.
Step-by-step explanation:
To solve for the perimeter of the rectangle, we need to find the dimensions of the rectangle, which are the length and the width. We are told the area of the rectangle is 600 m² and the length is six times the width. Let's denote the width as 'w' and the length as '6w'.
The area of a rectangle is calculated by multiplying the length by the width, so:
Area = length × width
600 m² = 6w × w
600 m² = 6w²
Dividing both sides of the equation by 6 gives:
w² = 100 m²
Taking the square root of both sides, we find:
w = 10 m
Now, knowing the width, we can find the length:
Length = 6w = 6 × 10 m = 60 m
The perimeter of a rectangle is calculated by adding the lengths of all four sides, which can be expressed as:
Perimeter = 2 × (length + width)
P = 2 × (60 m + 10 m) = 2 × 70 m = 140 m
Therefore, the perimeter of the rectangle is 140 meters.