In the figure above, ABC is similar to XYZ. If the length of side AB is 9 units, the length of side BC is 30 units, and the length of side YZ is 10 units, what is the length of side XY?
A.
5 units
B.
1 units
C.
6 units
D.
3 units
The figure is not visible but in similar triangles, corresponding sides are proportional.
The ratio of AB to BC (9/30 or 3/10) would be the same as the ratio of XY to YZ.
Let's denote XY as x. Then, we have:
x / 10 = 3 / 10
x = 3 units
So, the answer is D. 3 units.
Since triangle ABC is similar to triangle XYZ, the corresponding sides are proportional.
From the given information, we have:
AB/XY = BC/YZ
Substituting the known values, we get:
9/XY = 30/10
Simplifying the equation, we have:
9/XY = 3
Cross multiplying, we find:
3XY = 9
Dividing both sides by 3, we get:
XY = 3 units
Therefore, the length of side XY is 3 units.
To find the length of side XY, we need to use the concept of similarity between triangles. In similar triangles, corresponding sides are in proportion to each other.
In this case, we have triangles ABC and XYZ that are similar. This means that the ratio of the lengths of corresponding sides is equal. To find the length of side XY, we can set up the proportion using the lengths of corresponding sides:
AB/XY = BC/YZ
Substituting the given lengths:
9/XY = 30/10
Simplifying the equation:
9/XY = 3
Cross-multiplying:
3XY = 9
Solving for XY:
XY = 9/3 = 3 units
Therefore, the length of side XY is 3 units, which corresponds to option D.