, .
. . , , - .
,
.
.
:
1) KLM
= 17 , = 9 , = 10 , ML = 7,5 , LK = 6,75 , MK = 12,75
2)
= 4 , = 6, = 5, = 3 , = 2,5 , = 2
. .
.
, , ,
1) =9 ; =10 ; =17 ; LK=6,75 ; ML=7,5 ; MK=12,75
2) = 4 ; = 5; = 6; = 2 ; = 2,5 ; = 3
, , . .
1) AB / LK = 9 / 6,75 = 1 1/3 ! , . AB/ LK = BC / ML = AC / MK = 1 1/3
2) AB / MK = 4 / 2 = 2, AB / MK = BC / CK = AC / MC = 2
.
. . , . , - .
ABC A B, 12 8. .
.
BC. .
, AK - , ABC KAC - . , . , .
, ABC AKC :
AC: BC = KC: AC = AK: AB
AC: BC = KC: AC
8 / 12 = KC / 8
KC = 64 / 12 = 16 / 3
AKB = ABK (BK - , - AKB )
AK = BK
, BK = AC - KC,
AK = BK = 12 - 16 / 3
KC: AC = AK: AB
(16 / 3) / 8 = (12 - 16 / 3) / AB
AB = (AK * AC) / KC = 10
: 10
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.
, , . .
ABC A1B1C1 . 3:4. 14 2. .
- . h. S1=1/2ah, S2=1/2*3/4a*3/4h. , :
S1/S2 = 1/2 ah / (1/2 * 9/16 ah)
S1/S2 = ah / (9/16 ah)
S1/S2 = 16/9
, : " "
:
S1=16S2/9
S1-S2=14,
16S2/9-S2=14
7/9S2=14
S2=18, S1 = 14+18=32
: 18 32
AB DC ABCD , AB DC E. , 98 . , 5 7.
.
, EAD EBC. E, , , , AE DE , EAD EBC .
1.
E AD. BC, . EAD h1, EBC h2.
:
EAD SEAD=1/2*AD*h1.
EBC SEBC=1/2*BC*h2.
, . 5:7, . :
BC / AD = 5 / 7
BC = 5AD / 7
:
h2 / h1 = 5 / 7
h2 = 5h1 / 7
:
SEBC=1/2*BC*h2.
:
SEBC=1/2*(5AD / 7)*(5h1 / 7)
SEBC=1/2*AD*h1*25 / 49
, EAD 98 , SEAD=1/2*AD*h1.
:
SEBC = 98*25/49
SEBC = 50 2
2.
: " ", AED BEC 52: 72. :
SEBC / SEAD = 52 / 72
SEBC / SEAD = 25 / 49
SEBC = SEAD * 25 / 49
EAD 98 2,
SEBC = 98 * 25 / 49
SEBC = 50 2
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.
ABCD AED BEC. , 98 - 50 = 48 2.
: 48 2.