Question

(03 05 MC)

AABC is similar to AAXY by a ratio of 4:3. If BC= 24, what is the length of XY?
B
A
X

Answer 1

To find the length of side XY in the similar triangles ∆ABC and ∆AXY with a ratio of 4:3 and side BC measuring 24 cm, we use the similarity ratio to calculate XY, resulting in a length of 18 cm.

Step-by-step explanation:

The student asked about finding the length of side XY in a pair of similar triangles, given that ∆ABC is similar to ∆AXY by a ratio of 4:3 and that BC is 24 cm. To find XY, we use the similarity ratio:

Let the length of XY be y. Since the triangles are similar, the ratio of corresponding sides is the same, which means:

1. BC / XY = 4 / 3,
2. 24 / y = 4 / 3,
3. y = 24 × (3 / 4),
4. y = 18 cm.

Therefore, the length of XY is 18 cm.