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?(1 point)
Responses
Let the length of the shorter side be x inches. The length of the longer side would then be 2.5x inches.
The area of the window is given as 2,250 square inches. The formula for the area of a rectangle is length multiplied by width. So, we have:
x * 2.5x = 2,250
2.5x^2 = 2,250
Dividing both sides by 2.5, we get:
x^2 = 900
Taking the square root of both sides, we get:
x = 30
So, the dimensions of the window are 30 inches by 75 inches (2.5 times 30).
To find the dimensions of the window, we can set up a proportion using the given ratio of the lengths of the sides.
Let's let x represent the length of the shorter side of the rectangle.
Then, the length of the longer side would be 2.5x.
The area of a rectangle is found by multiplying the length and width, so we can set up the following equation:
x * (2.5x) = 2,250.
To solve this equation, we can simplify it by expanding the product on the left side:
2.5x^2 = 2,250.
Next, we divide both sides of the equation by 2.5 to isolate the x^2 term:
(2.5x^2) / 2.5 = 2,250 / 2.5.
This simplifies to:
x^2 = 900.
To find the value of x, we can take the square root of both sides of the equation:
√(x^2) = √900.
This simplifies to:
x = 30.
Therefore, the shorter side of the rectangle is 30 inches, and the longer side is (2.5 * 30) = 75 inches.
So, the dimensions of the window are 30 inches by 75 inches.
To find the dimensions of the rectangular window, we need to use the information given about the ratio of the side lengths and the area of the window.
Let's assume that the length of the window is represented by 2.5x, where x is a constant, and the width of the window is represented by x.
We know that the area of a rectangle is given by the formula: Area = Length x Width.
Since the area of the window is given as 2,250 square inches, we can set up the equation:
2.5x * x = 2,250
Simplifying the equation, we have:
2.5x^2 = 2,250
To solve for x, we can divide both sides of the equation by 2.5:
x^2 = 2,250 / 2.5
x^2 = 900
Taking the square root of both sides, we get:
x = √900
x = 30
Now that we have the value of x, we can find the dimensions of the window:
Length of the window = 2.5x = 2.5 * 30 = 75 inches
Width of the window = x = 30 inches
Therefore, the dimensions of the window are 75 inches by 30 inches.