Final answer:
To find the rectangle's dimensions, set up the equation 128=2(5x)+2(3x), simplify to 128=16x, solve for x=8, and then calculate length as 5x=40 meters and width as 3x=24 meters.
Step-by-step explanation:
To find the length and width of the rectangle with a perimeter of 128 meters and a ratio of length to width of 5:3, we first need to set up two equations. The perimeter (P) of a rectangle is given by P = 2l + 2w, where l is the length and w is the width. Using the given perimeter of 128 meters and the ratio of 5:3, we can express the length as 5x and the width as 3x, where x is the common multiplier. Therefore, the perimeter equation becomes 128 = 2(5x) + 2(3x).
After simplifying the equation, we get 128 = 10x + 6x, which means that 128 = 16x. Dividing both sides by 16 gives us x = 8. Consequently, the length is 5x = 40 meters and the width is 3x = 24 meters.