The lengths of the sides of a rectangular window have a ratio 1.5 to 1. The area of the window is 1,350 square inches. What are the dimensions of the window?
30 inches by 45 inches
30 inches by 60 inches
30 inches by 90 inches
30 inches by 22.5 inch
Let's assume that the shorter side of the window is x inches.
Since the lengths of the sides of the window have a ratio of 1.5 to 1, we can express the longer side as 1.5x inches.
The area of a rectangle is given by the formula: length x width.
In this case, the area is 1,350 square inches, so we have the equation:
x * 1.5x = 1,350
1.5x^2 = 1,350
x^2 = 900
x = √900
x = 30
Therefore, the shorter side of the window is 30 inches.
The longer side is 1.5x, which is 1.5 * 30 = 45 inches.
The dimensions of the window are 30 inches by 45 inches.
Therefore, the correct option is: 30 inches by 45 inches.