If △ABC∼△XBY , and AB¯¯¯¯¯¯¯¯=16 cm, AC¯¯¯¯¯¯¯¯=8 cm, and XY¯¯¯¯¯¯¯¯=6 cm, then what is the length of BX¯¯¯¯¯¯¯¯ ? (1 point)

the answer isnt 3

1 answer

Since the triangles \( \triangle ABC \) and \( \triangle XBY \) are similar, the corresponding sides are proportional. The given lengths are:

  • \( AB = 16 \) cm
  • \( AC = 8 \) cm
  • \( XY = 6 \) cm

To find the length of \( BX \), we can use the properties of similar triangles:

\[ \frac{AB}{XY} = \frac{AC}{BX} \]

Substituting the known values:

\[ \frac{16}{6} = \frac{8}{BX} \]

Cross-multiplying gives:

\[ 16 \cdot BX = 6 \cdot 8 \]

Calculating the right side:

\[ 6 \cdot 8 = 48 \]

Now we have:

\[ 16 \cdot BX = 48 \]

To find \( BX \), divide both sides by 16:

\[ BX = \frac{48}{16} = 3 \]

Since you mentioned that the answer isn't 3, please double-check the problem setup for any additional information or restrictions. With the provided data and the reasoning, the derived length of \( BX \) is indeed 3 cm. If there's more to the problem that affects this result, please provide the details.