Question

На рисунке af=35 ac=12 bd=11 ce=12 df=16.чему равна длина отрезка be? схема: варианты ответа: (а)17 (б)16 ( в )15 ( г )14 ( д)13

Answer 1

AB + BC = 12 => BC = 12 - AB (1)
BC + CD = 11 => BC = 11 - CD (2)
CD + DE = 12 => DE = 12 - CD (3)
DE + EF = 16 => DE = 16 - EF (4)

Ур-ния (1) = (2) и (3) = (4) =>
12 - AB = 11 - CD => AB - CD = 1 => CD = AB - 1
12 - CD = 16 - EF => EF - CD = 4 =>
EF = 4 + CD = 4 + (AB-1) = 3 + AB
DE = 12 - CD = 12 - (AB-1) = 13 - AB

AB - 1= EF - 4 => EF = AB + 3

AB + BC + CD + DE + EF = 35
= AB + (12 - AB) + (AB - 1) + (13 - AB) + (AB + 3) = 35
AB + 12 - AB + AB - 1 + 13 - AB + AB + 3 = 35
AB = 8
BC = 12 - AB = 12 - 8 = 4
CD = AB - 1 = 8 - 1 = 7
DE = 13 - AB = 13 - 8 = 5
EF = AB + 3 = 8 + 3 = 11
8 + 4 + 7 + 5 + 11 = 35