rectangular cake pans X and Y are similar. The ratio of the width of pan X to the width of pan Y is 3:4. the length of pan X is 10 inches and its width is 5 inches. what is the perimeter of pan Y.
all dimensions of pan y are 4/3 times the corresponding dimension of pan x
length y = 4/3 *10 = 40/3
width y = 4/3 * 5 = 20/3
twice length + twice width = 80/3+40/3 = 120/3 = 40
I threw a grape at a squirrel's butt today.
To find the perimeter of pan Y, we need to determine its dimensions based on the given information.
We're told that pan X has a width of 5 inches and a length of 10 inches. Let's use these measurements to find the dimensions of pan Y.
Since the ratio of the width of pan X to the width of pan Y is 3:4, we can set up the following proportion:
5 inches (width of pan X) / x inches (width of pan Y) = 3/4
To solve for x, we can cross multiply:
5 * 4 = 3 * x
20 = 3x
Dividing both sides of the equation by 3:
20/3 = x
So, the width of pan Y is approximately 6.67 inches.
Since pan Y is similar to pan X and we have the ratio of their widths, we can also determine the length of pan Y using the same ratio:
10 inches (length of pan X) / y inches (length of pan Y) = 3/4
Cross multiplying:
10 * 4 = 3 * y
40 = 3y
Dividing both sides of the equation by 3:
40/3 = y
So, the length of pan Y is approximately 13.33 inches.
Now that we have the dimensions of pan Y (length: 13.33 inches, width: 6.67 inches), we can calculate its perimeter.
The formula for the perimeter of a rectangle is: P = 2 * (length + width)
Substituting in the values:
P = 2 * (13.33 + 6.67)
P = 2 * (20)
Calculating the final result:
P = 40 inches
Therefore, the perimeter of pan Y is 40 inches.
To find the perimeter of pan Y, we need to know the dimensions of pan Y.
Given that pan X and pan Y are similar, we can set up the following proportion:
width of pan X : width of pan Y = 3 : 4
We are given that the width of pan X is 5 inches, so we can substitute this value into the proportion:
5 : width of pan Y = 3 : 4
To find the width of pan Y, we can cross-multiply and solve for it:
5 * 4 = 3 * width of pan Y
20 = 3 * width of pan Y
Next, we divide both sides of the equation by 3 to isolate the width of pan Y:
20 / 3 = width of pan Y
Now we know that the width of pan Y is approximately 6.67 inches.
Given that the length of pan X is 10 inches, we can assume that the length of pan Y is also in the same ratio of 3:4. So, we can set up another proportion:
length of pan X : length of pan Y = 3 : 4
Substituting the values, we get:
10 : length of pan Y = 3 : 4
Similarly, we can solve for the length of pan Y using cross-multiplication:
10 * 4 = 3 * length of pan Y
40 = 3 * length of pan Y
Dividing both sides of the equation by 3, we get:
40 / 3 = length of pan Y
Now we know that the length of pan Y is approximately 13.33 inches.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
Substituting the values, we have:
Perimeter of pan Y = 2 * (13.33 + 6.67)
Perimeter of pan Y = 2 * 20
Perimeter of pan Y = 40 inches
Therefore, the perimeter of pan Y is 40 inches.