Final answer:
To find the dimensions of the rectangle, set up a proportion using the given ratio of length to width and solve for x. Substitute the value of x back into the ratio to find the length and width of the rectangle.
Step-by-step explanation:
To find the dimensions of the rectangle, we need to set up a proportion using the given ratio of length to width. Let's call the length L and the width W. The given ratio is L:W = 3:2. Since the perimeter of the rectangle is 150 centimeters, we can write the equation 2(L + W) = 150. Now, substitute L = 3x and W = 2x into the equation and solve for x.
2(3x + 2x) = 150
10x = 150
x = 15
So, the length of the rectangle is L = 3x = 3(15) = 45 centimeters, and the width is W = 2x = 2(15) = 30 centimeters.