Final answer:
The length of base WX of trapezoid WXYZ is found to be 1.25 cm by using the mid-segment formula, which equals the average of the two bases. Since the mid-segment is given as 2.75 cm and the other base as 4.25 cm, WX can be calculated and is found to be 1.25 cm.
Step-by-step explanation:
The question asks to find the length of the base WX of trapezoid WXYZ given the length of the mid-segment and the other base YZ. The mid-segment of a trapezoid is the segment that connects the midpoints of the non-parallel sides, and its length is the average of the lengths of the two bases. Since we know YZ = 4.25 cm and the mid-segment is 2.75 cm long, we calculate WX using the formula:
- Mid-Segment = (Base1 + Base2)/2
- 2.75 cm = (WX + 4.25 cm)/2
- 2.75 cm × 2 = WX + 4.25 cm
- 5.5 cm = WX + 4.25 cm
- WX = 5.5 cm - 4.25 cm
- WX = 1.25 cm
Therefore, the length of base WX of the trapezoid is 1.25 centimeters.