Question

Δabc is similar to Δaxy by a ratio of 3:2. If ac = 18, what is the length of ay?

1) 4.5
2) 6
3) 9
4) 12

Answer 1

To find the length of side AY in ΔAXY, given that ΔABC is similar to ΔAXY by a ratio of 3:2, and AC is 18, we set up a proportion between the sides of the triangles and solve for AY, which gives us 12 units.

Step-by-step explanation:

The question asks to find the length of AY in triangle ΔAXY, given that triangle ΔABC is similar to ΔAXY with a ratio of 3:2 and that AC is 18 units. To solve this, we use the concept of similar triangles which maintains that corresponding sides are proportional. Since the ratio of similarity is 3:2, this means that for every 3 units in ΔABC, there are 2 units in ΔAXY.

Therefore, using the formula for proportional sides of similar triangles, if AC in ΔABC is 18 units, and AY corresponds to AC in triangle ΔAXY, we have the following proportion:

1. Set up the proportion: (length of AC) / (length of AY) = (ratio of ΔABC) / (ratio of ΔAXY)
2. Substitute the known values: 18 / AY = 3 / 2
3. Solve for AY: AY = (18 * 2) / 3
4. Calculate the value of AY: AY = 36 / 3 = 12

Therefore, the length of AY is 12 units.