Whats the right answer
The lengths of the sides of a rectangular window have the ratio 1.5 to 1. The area of the window is 1,350 square inches. What are the dimensions of the window?
(1 point)
Responses
30 inches by 45 inches
30 inches by 45 inches
30 inches by 60 inches
30 inches by 60 inches
30 inches by 90 inches
30 inches by 90 inches
30 inches by 22.5 inches
The correct answer is 30 inches by 45 inches.
To find the dimensions of the window, we need to first determine the length of the shorter side.
Let's assume that the shorter side of the window is x inches. Since the lengths of the sides have a ratio of 1.5 to 1, the longer side would be 1.5x inches.
The area of a rectangle is given by the formula length * width. In this case, the area is 1,350 square inches. So we can set up the following equation:
x * 1.5x = 1,350
If we simplify the equation, we get:
1.5x^2 = 1,350
Now we can solve for x by dividing both sides of the equation by 1.5:
x^2 = 900
Taking the square root of both sides, we find:
x = √900
x = 30
So the shorter side of the window is 30 inches. The longer side would then be 1.5 times the shorter side, which is:
1.5 * 30 = 45
Therefore, the dimensions of the window are 30 inches by 45 inches.
The correct answer is:
30 inches by 45 inches
To find the dimensions of the window, we can use the information given in the question. Let's break down the problem step by step.
Step 1: Understand the problem
We know that the lengths of the sides of the window have a ratio of 1.5 to 1. This means that one side is 1.5 times longer than the other side.
Step 2: Set up equations
Let's assume the shorter side of the window is x inches. This means the longer side would be 1.5x inches. We can use these lengths to calculate the area of the window.
The area of a rectangle is given by the formula: Area = length × width
So, in this case, the equation becomes:
Area = x × 1.5x = 1,350 square inches
Step 3: Solve the equation
To solve the equation, let's multiply the lengths:
1.5x^2 = 1,350
Step 4: Divide both sides by 1.5
To isolate the variable, divide both sides of the equation by 1.5:
x^2 = 900
Step 5: Take the square root of both sides
To solve for x, take the square root of both sides:
x = √900
x = 30
So, the shorter side of the window is 30 inches.
Step 6: Calculate the longer side
Since we know that the longer side is 1.5 times the shorter side, we can multiply 30 by 1.5:
Longer side = 30 × 1.5 = 45 inches
Therefore, the dimensions of the window are 30 inches by 45 inches.
The correct answer is: 30 inches by 45 inches.