Points D, C and E lie on the segment AB. Point D is the middle of the segment AC and point E is the middle of the segment

Points D, C and E lie on the segment AB. Point D is the middle of the segment AC and point E is the middle of the segment СВ. The distance between points D and E is 16 cm. Find the length of the segment AB.

From the condition it is known that D is the middle of the segment AC, based on these data, we can assume that the segment AD is equal to the segment DC.

It is also known that E is the middle of the segment CB, based on these data, it can be seen that the segment CE is equal to the segment EB.

Now we can see that the length of the segment DE is a part of the lengths of the segments DC and CE, and the length of the segment AB is a part of the lengths of the segments CE, DC, EB and AD.

From all the data it can be seen that the length of the segment AB corresponds to the two lengths of the segment DC and CE.

We can find the length AB.

AB = DE * 2 = 16 * 2 = 32 (centimeters) – the length of the segment AB.

Answer: the length of the segment AB is 32 centimeters.



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