Polygon ABCD is similar to polygon WXYZ. If AB = 8, WX = 12, and CD = 10, find YZ.
AB / WX = CD / YZ , 8 / 12 = 10 / YZ.
YZ = 15.
Well, if polygons ABCD and WXYZ are similar, that means their corresponding sides are proportional. So, we can set up a proportion to find out the length of YZ.
AB/ WX = CD/ YZ
Plugging in the values we know:
8/12 = 10/YZ
Now let's cross multiply and solve for YZ:
12*10 = 8*YZ
120 = 8*YZ
Dividing both sides by 8:
120/8 = YZ
15 = YZ
So, it looks like YZ is 15!
To find the length of YZ, we can use the concept of similarity ratios.
Since polygon ABCD is similar to polygon WXYZ, corresponding lengths on the polygons are proportional.
The similarity ratio between the two polygons is the scale factor of their corresponding sides.
The scale factor, denoted as k, can be found by comparing the lengths of any pair of corresponding sides.
In this case, we can compare AB and WX.
AB/WX = CD/YZ
Substituting the given values:
8/12 = 10/YZ
We can cross-multiply to solve for YZ:
8 * YZ = 12 * 10
8 * YZ = 120
Dividing both sides by 8:
YZ = 120/8
YZ = 15
Therefore, the length of YZ is 15.
To determine the length of YZ, you need to establish a proportion between corresponding sides of the similar polygons.
In a pair of similar polygons, corresponding sides are proportional, which means that:
AB/WX = CD/YZ
Given AB = 8, WX = 12, and CD = 10, you can substitute these values into the above proportion:
8/12 = 10/YZ
To isolate YZ, you can cross-multiply:
8 * YZ = 12 * 10
Simplifying, we get:
8YZ = 120
To solve for YZ, divide both sides by 8:
YZ = 120/8
Therefore, YZ = 15. So the length of segment YZ is 15 units.