Answer:
Step-by-step explanation:
Given that the area of the rectangle is 720 sqft and the ratio of length to width is 3:5, we can set up the equation:
length * width = area
Let's assign variables to the length and width:
length = 3x
width = 5x
Substituting these values into the equation:
(3x) * (5x) = 720
15x^2 = 720
To solve for x, we divide both sides of the equation by 15:
x^2 = 48
Taking the square root of both sides:
x = √48
Simplifying:
x = 4√3
Now we can find the length and width:
length = 3x = 3 * 4√3 = 12√3
width = 5x = 5 * 4√3 = 20√3
To find the perimeter, we add the lengths of all sides:
perimeter = 2(length + width) = 2(12√3 + 20√3) = 2(32√3) = 64√3
Therefore, the perimeter of the rectangle is 64√3 sqft.
