To find the dimensions of the rectangular window, we start by letting the length of the window be represented as 15x and the width as 1x, based on the given ratio of 15 to 1.
The area of a rectangle is calculated by multiplying its length by its width. Therefore, we can set up the following equation based on the area:
Area = Length × Width
1350 = (15x) × (1x)
This simplifies to:
1350 = 15x²
Next, we solve for x²:
x² = 1350 / 15
x² = 90
Now, we take the square root of both sides to find x:
x = √90
We can simplify √90 to 3√10, but for practical purposes, we can also use the approximate value:
x ≈ 9.49
Now that we have x, we can find the dimensions of the window:
- Length = 15x ≈ 15 × 9.49 ≈ 142.35 inches
- Width = 1x ≈ 9.49 inches
Thus, the dimensions of the window are approximately 142.35 inches by 9.49 inches.