Question

Line segment ABCD is split into unequal segments by points A, B, C, and D. The length of segment AD is 28 cm, and the distance between the midpoints of segments AB and CD is 16 cm. Find the length of segment BC.

Answer 1

4 cm

Explanation:

The midpoint segment has length ...

... L = AB/2 + BC + CD/2 = 16 cm

The entire segment has length ...

... AD = AB + BC + CD = 28 cm

If we subtract AD from 2L, we have ...

... 2L - AD - 2L = 2(AB/2 +BC + CD/2) - (AB +BC +CD) = 2(16 cm) -28 cm = 4 cm

... AB +2BC + CD -AB -BC -CD = 4 cm . . . . remove parentheses

... BC = 4 cm . . . . simplify