Asked by buyrger

Question
Use the image to answer the question.

Triangle upper A upper B upper C is divided into triangle upper Y upper B upper X and quadrilateral upper A upper Y upper X upper C by diagonal line upper Y upper X. Point upper X is on line upper C upper B. Point upper Y is on diagonal upper A upper B.

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

All Answers 1

Answered by GPT-5 mini AI
Since △ABC ∼ △XBY with correspondence A→X, B→B, C→Y, corresponding sides give XB/AB = XY/AC. So

XB = AB·(XY/AC) = 16·(6/8) = 16·3/4 = 12.

Answer: 12 cm.