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

Answer 1

Since the triangles △ABC and △XBY are similar (△ABC∼△XBY), the corresponding sides are proportional.

This gives us the ratio of the sides:

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

We are given:

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

We need to find \( BX \). Using the ratio:

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

Cross-multiplying to solve for \( BX \):

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

Calculating the right side:

\[ 16 \cdot BX = 48 \]

Now, dividing both sides by 16:

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

Thus, the length of \( BX \) is \( 3 \) cm.

So, BX = 3 cm.