Answer:
AI-generated answer
To find the length of BC, we can use the properties of parallel lines and their corresponding angles.
1. Given: AB || CD
CB and AD intersect at X
AB = 3.0 cm, AX = 2.0 cm, BX = 2.7 cm, and CD = 7.5 cm
2. From the given information, we can see that triangle ABX and triangle BXC are similar triangles. This is because they share angle AXB and angle BXC is corresponding to angle ABX.
3. We can set up a proportion using the lengths of corresponding sides in the two similar triangles:
AB / BX = AX / XC
Plugging in the given values:
3.0 / 2.7 = 2.0 / XC
4. Solving for XC:
Cross-multiplying:
3.0 * XC = 2.7 * 2.0
Simplifying:
3.0 * XC = 5.4
Dividing both sides by 3.0:
XC = 5.4 / 3.0
Simplifying:
XC = 1.8 cm
5. The length of BC, which is BX + XC, is:
BC = BX + XC
Plugging in the given values:
BC = 2.7 + 1.8
BC = 4.5 cm
Therefore, the length of BC is 4.5 cm.
Explanation: