The 42 cm segment is divided into three (not necessarily equal) segments; the distance between the midpoints

| April 2, 2021 | education

The 42 cm segment is divided into three (not necessarily equal) segments; the distance between the midpoints of the outermost segments is 26 cm. Find the length of the middle segment.

Let’s find how long both halves of the extreme segments are. Subtract from the length of the total segment the length between the centers of the segments that are at the edges:

42 – 26 = 16 cm.

Next, we determine the length between the center of the extreme segment to the edge of the common segment. The same length will be from the center of the outermost segments to the edges of the middle segment. Divide the sum of the lengths of the halves of the extreme segments by 2:

16: 2 = 8 cm from the middle of the outermost segments to the edges of the middle segment.

Now, from the length between the centers of the extreme segments, we subtract the length of the two halves of the extreme segments. So we get the length of the middle segment:

26 – 8 * 2 = 26 – 16 = 10 cm

Answer: 10 cm.



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