Right triangle ABC is similar to triangle XYZ, because angle B is congruent to angle Y. If side AB equals 15 inches, side BC equals 45 inches, and side YZ equals 9 inches, then what is the length of side XY?
XY/AB = YZ/BC,
XY/15 = 9/45,
Multiply both sides by 15:
XY = 135/45 = 3.
To find the length of side XY, we can set up a proportion using the corresponding sides of the similar triangles.
Since triangle ABC is similar to triangle XYZ, we can write the following proportion:
AB/XY = BC/YZ
Substituting the given values:
15/XY = 45/9
To solve for XY, we can cross multiply:
15 * 9 = 45 * XY
135 = 45 * XY
Now, we can solve for XY by dividing both sides of the equation by 45:
XY = 135/45
Simplifying:
XY = 3
Therefore, the length of side XY is 3 inches.