In the figures below, ABCD~WXYZ has a scale factor of 3:1. If the perimeter of ABCD is 66 units, find the perimeter of WXYZ.
No figures. Cannot copy and paste here.
three times 66 = 198
If the scale is 3/1 then all corresponding dimensions are 3 times as large in the big one.
Areas are 3*3 = 9 times
Volumes are 3*3*3 = 27 times
To find the perimeter of WXYZ, we can use the scale factor to determine the ratio of their perimeters.
The scale factor of 3:1 means that the corresponding sides of ABCD and WXYZ are in the ratio of 3:1. Thus, each side of WXYZ is 1/3 the length of the corresponding side of ABCD.
If the perimeter of ABCD is 66 units, we can find the length of each side of ABCD by dividing the perimeter by 4 (since ABCD is a quadrilateral with four sides).
Each side of ABCD is 66/4 = 16.5 units long.
Therefore, each side of WXYZ is 1/3 * 16.5 = 5.5 units long.
Since WXYZ is also a quadrilateral with four sides, the perimeter of WXYZ is 4 * 5.5 = 22 units.
To find the perimeter of WXYZ, we can use the scale factor relationship and the fact that corresponding sides of similar figures are proportional.
Given that the scale factor of ABCD to WXYZ is 3:1, we know that corresponding sides of both figures are in a 3:1 ratio. This means that for every 3 units of length in ABCD, there is 1 unit of length in WXYZ.
Since the perimeter of ABCD is 66 units, we can assume that each side of ABCD is equal in length, and therefore, the length of each side is 66 / 4 = 16.5 units.
Now, using the scale factor, we can find the length of the corresponding sides in WXYZ. Each side in WXYZ is 1/3 the length of the corresponding side in ABCD.
Therefore, the length of each side in WXYZ is (1/3) * 16.5 = 5.5 units.
Since WXYZ is also a quadrilateral, just like ABCD, its perimeter is the sum of all its side lengths.
Therefore, the perimeter of WXYZ is 4 * 5.5 = 22 units.