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 ?
a. 30 inches by 45 inches
b. 30 inches by 60 inches
c. 30 inches by 90 inches
d. 30 inches by 22.5 inches

Let the smaller length be a. Then the larger length will be 1.5a.
Now we can write the equation:

which simplifies to

Therefore choice A is the correct answer.

There are numerous information's already given in the question. Based on these information's the answer can be easily deduced.
Let us assume the length of the smaller side = x
Then
Length of the longer side of the rectangle = 1.5x
Area of the window = 1350 square inches
So
1.5x * x = 1350
1.5x^2 = 1350
x^2 = 1350/1.5
x^2 = 900
x = 30 inches
Then
Length of the longer side = 1.5 * 30 inches
                                        = 45 inches
From the above deduction, we can conclude that the correct option among all the options that are given in the question is the first option or option "A".