The lengths of the sides of a rectangular window have the ratio 2.5 to 1. The area of the window is 2,250 square inches. What are the dimensions of the window?
Let the length of the window be 2.5x and the width of the window be 1x.
The area of the window is length x width, so we have (2.5x)(1x) = 2,250.
Expanding the equation gives 2.5x^2 = 2,250.
Dividing both sides of the equation by 2.5 gives x^2 = 900.
Taking the square root of both sides gives x = 30.
Thus, the width of the window is 30 inches and the length of the window is 2.5(30) = 75 inches.
To find the dimensions of the rectangular window, we need to use the given information about the ratio of the lengths of the sides and the area of the window.
Step 1: Let's represent the length of the window as 2.5x and the width as 1x, where x is a variable representing a common factor.
Step 2: The formula for the area of a rectangle is length multiplied by width. In this case, the area of the window is given as 2,250 square inches. So we can write the equation:
(2.5x) * (1x) = 2250
Step 3: Simplify the equation:
2.5x * x = 2250
2.5x^2 = 2250
Step 4: Divide both sides of the equation by 2.5 to solve for x:
x^2 = 2250 / 2.5
x^2 = 900
Step 5: Take the square root of both sides to find the value of x:
x = √900
x = 30
Step 6: Substitute the value of x back into the length and width equations:
Length = 2.5x = 2.5 * 30 = 75 inches
Width = 1x = 1 * 30 = 30 inches
Therefore, the dimensions of the window are 75 inches by 30 inches.
To find the dimensions of the window, we need to set up and solve an equation based on the given information.
Let's say the length of the window is L inches, and the width of the window is W inches.
From the problem, we know that the ratio of the lengths is 2.5 to 1. This can be written as:
L/W = 2.5/1
We also know that the area of the window is 2,250 square inches. The area of a rectangle is calculated by multiplying the length by the width. So, we can write another equation:
L * W = 2,250
Now we have a system of two equations:
1) L/W = 2.5/1
2) L * W = 2,250
To solve this system, we can rearrange the first equation to express L in terms of W:
L = (2.5/1) * W
Substituting this value of L into the second equation, we get:
(2.5/1) * W * W = 2,250
Now we can solve for W by multiplying:
2.5 * W^2 = 2,250
Rearranging this equation, we have:
W^2 = 2,250 / 2.5
W^2 = 900
Taking the square root of both sides, we find:
W = √900
W = 30
Now, substituting this value of W back into the first equation, we can solve for L:
L = (2.5/1) * 30
L = 75
Therefore, the dimensions of the window are 75 inches by 30 inches.