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 ?
X is 5 by 10
Y:x = 4/3, so
Y is 20/3 by 40/3
and its perimeter is thus 40
or
X is 5 by 10,
so its perimeter is 30
Y:X = 4:3, so its perimeter is 40
i stiill dont understand, can u explan again
To find the perimeter of pan Y, we need to determine its dimensions. Since the cake pans are similar, we can set up a proportion to find the width of pan Y.
The ratio of the width of pan X to pan Y is given as 3:4. We can set up the proportion as follows:
Width of pan X / Width of pan Y = 3 / 4
Plugging in the values we know:
5 inches (Width of pan X) / Width of pan Y = 3 / 4
To solve for the width of pan Y, we cross-multiply:
4 * 5 inches = 3 * Width of pan Y
20 inches = 3 * Width of pan Y
Divide both sides of the equation by 3:
Width of pan Y = 20 inches / 3
Width of pan Y ≈ 6.67 inches (rounded to two decimal places)
Now that we have the width of pan Y, we can find its length.
Since the pans are similar, the ratio of length X to length Y is the same as the ratio of the width X to width Y:
Length of pan X / Length of pan Y = Width of pan X / Width of pan Y
Plugging in the known values:
10 inches (Length of pan X) / Length of pan Y = 5 inches (Width of pan X) / 6.67 inches (Width of pan Y)
To solve for the length of pan Y, we cross-multiply:
5 inches * Length of pan Y = 6.67 inches * 10 inches
Length of pan Y = (6.67 inches * 10 inches) / 5 inches
Length of pan Y = 13.34 inches
Now that we have the width and length of pan Y, we can calculate its perimeter.
The perimeter of a rectangle is the sum of all its sides. Since a rectangle has two equal pairs of sides, we can use the formula:
Perimeter of pan Y = 2 * (Width of pan Y + Length of pan Y)
Plugging in the values we found:
Perimeter of pan Y = 2 * (6.67 inches + 13.34 inches)
Perimeter of pan Y = 2 * 20.01 inches
Perimeter of pan Y ≈ 40.02 inches (rounded to two decimal places)
Therefore, the perimeter of pan Y is approximately 40.02 inches.