The lengths of the sides of a rectangular window have the 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 inches
Let's assume that the shorter side of the rectangular window is x inches.
According to the given information, the lengths of the sides of the window have a ratio of 1.5 to 1, or x:1.5x.
The area of the window is given as 1,350 square inches.
To find the dimensions of the window, we can use the formula for the area of a rectangle: A = length * width.
Substituting the given values, we get:
1,350 = x * (1.5x)
Simplifying the equation, we get:
1,350 = 1.5x^2
Dividing both sides of the equation by 1.5, we get:
900 = x^2
Taking the square root of both sides, we get:
x = 30
So, the shorter side of the window is 30 inches.
The longer side of the window is 1.5 times the shorter side:
1.5x = 1.5 * 30 = 45
Therefore, the dimensions of the window are 30 inches by 45 inches.
The correct answer is 30 inches by 45 inches.