To find the dimensions of the rectangular window, we first need to understand the given information. The ratio of the lengths of the sides is 16 to 1, which means that if we let the width be represented as ‘w’, then the length can be represented as ’16w’.
Next, we can use the formula for the area of a rectangle, which is:
Area = Length × Width
Given that the area of the window is 2560 square inches, we can set up the equation:
2560 = (16w) × w
This simplifies to:
2560 = 16w2
To isolate ‘w’, we divide both sides of the equation by 16:
w2 = 2560 / 16
w2 = 160
Now, we take the square root of both sides to solve for ‘w’:
w = √160
w = 4√10
(approximately 12.65 inches). Now we can find the length:
Length = 16w = 16 × 4√10 = 64√10
(approximately 40.51 inches). Hence, the dimensions of the window are:
Width: 4√10 inches (about 12.65 inches) and Length: 64√10 inches (about 40.51 inches).