Right triangle ABC is similar to triangle XYZ. If the length of side AB is 30 inches, the length of side BC is 60 inches, and the length of side YZ is 10 inches, what is the length of side XY?
A.4
B.7
C.6
D.none of above
To find the length of side XY, we can use the concept of proportions since the triangles are similar.
The proportion for similar triangles states that the ratio of corresponding sides is equal.
In this case, we have:
AB/XY = BC/YZ
Substituting the given values:
30/XY = 60/10
Now, we can solve for XY by cross multiplying and then dividing:
10 * 30 = 60 * XY
300 = 60XY
Finally, we can solve for XY:
XY = 300/60
XY = 5
So, the length of side XY is 5 inches.
However, none of the given options (A, B, C) match the calculated length. Therefore, the correct answer would be D, none of the above.
To determine the length of side XY, we can use the concept of similarity between triangles. When two triangles are similar, their sides are proportional in length.
In this case, we can set up a proportion using the corresponding sides of the two triangles:
AB/XY = BC/YZ
Substituting the given values, we have:
30/XY = 60/10
To solve for XY, cross-multiply and then divide:
30 * 10 = 60 * XY
300 = 60 * XY
XY = 300 / 60
XY = 5 inches
Therefore, the length of side XY is 5 inches. None of the given options (A, B, C, D) match the correct answer.
use pythagorean theorem!
a^2 + b^2 = c^2
actually, use similar triangles.
XY:AB = YZ:BC
XY:30 = 10:60
XY=5
so, (D)