the lengths of the sides of rectangular window have the ratio 2.5 to 1 the area of window is 2,250 square inches what are the dimensions of the window
A 30inches by 75 inches
B 60 inches by 37.5 inches
C 30 inches by 45inches
D 50 inches by 45inches
Let's assume that the shorter side of the rectangle is x inches.
According to the given ratio of 2.5 to 1, the longer side would be 2.5x inches.
The area of the rectangle is length × width = x × 2.5x = 2.5x^2.
We are given that the area is 2,250 square inches, so:
2.5x^2 = 2,250
Dividing both sides of the equation by 2.5:
x^2 = 900
Taking the square root of both sides:
x = 30
Therefore, the dimensions of the window are:
Shorter side: 30 inches
Longer side: 2.5x = 2.5(30) = 75 inches
So, the correct answer is A) 30 inches by 75 inches.
To find the dimensions of the window, we can solve the problem step by step.
Step 1: Set up ratios
The ratio of the lengths of the sides is given as 2.5 to 1. Let's call the length of one side x and the length of the other side 2.5x.
Step 2: Formulate an equation
The area of a rectangle is given by multiplying the length by the width. So, we have x * (2.5x) = 2250.
Step 3: Solve the equation
Multiply 2.5x by x to get 2.5x^2 = 2250.
Divide both sides by 2.5 to isolate x^2: x^2 = 900.
Take the square root of both sides to solve for x: x = √900 = 30.
Step 4: Find the dimensions
We found that x = 30. Now we can find the dimensions by substituting this value back into our ratios.
The width (x) is 30 inches.
The length (2.5x) is 2.5 * 30 = 75 inches.
Therefore, the dimensions of the window are 30 inches by 75 inches.
So, the correct option is A: 30 inches by 75 inches.
To find the dimensions of the window, we can set up equations based on the given information.
Let's assume that the length of the window is represented by "2.5x" and the width is represented by "x", where "x" is a constant.
According to the given ratio, we have:
Length : Width = 2.5x : x
We also know that the area of the window is 2,250 square inches:
Area = Length * Width
2250 = (2.5x) * x
To solve for "x", we can rearrange the equation:
2.5x * x = 2250
2.5 * x^2 = 2250
x^2 = 2250 / 2.5
x^2 = 900
x = sqrt(900)
x = 30
Therefore, the width of the window is 30 inches.
Now, we can substitute this value of "x" back into the length equation:
Length = 2.5x
Length = 2.5 * 30
Length = 75
Therefore, the dimensions of the window are 30 inches by 75 inches.
So, the correct option is A) 30 inches by 75 inches.