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 b

Question

2 years ago

10

etween the midpoints of segments AB and CD is 16 cm. Find the length of segment BC.

1 answer:

Oksana_A [137] · Answer 1 · 2022-05-17T18:46:14+03:00

Answer:

4 cm

Step-by-step 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