379, 381, 383, 384

ա)

AB = 10

BC = DA = 13

CD = 20

AB = HE = 10

DH = EC = (20 — 10)/2 = 5

BE2 = BC2 — EC2 = 169 — 25 = 144

BE = √144 = 12

S = 10 + 20/2 * 12 = 180սմ²

բ)

<C = < D = 60^o

AB = BC = 8

<EBC = 180 — (90 + 60) = 30^o

EC = DH = 8:2 = 4

BE2 = BC2 — EC2 = 64 — 16 = 48

BE = √48 = 16 * 3 = 4√3

DC = 8 + 4 * 2 = 16

S = (16 + 8)/2 * 4√3 = 48√3

գ)

<C = <D = 45^o

AB = 6

BC = 9√2

AB = HE = 6

BC = AD = 9√2

BE = EC = AH = DH = x

x2 + x2 = 162

2×2 = 162

x2 = 162/2 = 81

√81 = 9

BC = 8 + 9 + 9 = 26

S = 8 + 26/2 * 9 = 153սմ²

ա) 6, 8, 10

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բ) 5, 6, 7

Ոչ

գ) 9, 12, 15

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դ) 10, 24, 26

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ե) 3, 4, 6

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զ) 11, 9, 13

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է) 15, 20, 25

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ա)

AB = 7

BC = 25

AC = 24

AD = ?

AD2 = AB2 — BD2 = AB2 — (BC — BD)2 = 49 — (25 — CD)2 = 49 — 625 + 50CD — CD2

AD2 = AC2 — CD2 = 576 — CD2

49 — 625 + 50CD — CD2 = 576 — CD2

-576 + 50CD = 576

50CD = 576 + 576 = 1152

CD = 1152/50 = 23,04

AD2 = AC2 — CD2 = 576 — 531 = 45

AD = √45 = √9 * √5 = 3√5

բ)

AB = 8

BC = 17

AC = 15

AD = ?

AD2 = AB2 — BD2 = AB2 — (BC — BD)2 = 64 — (17 — CD)2 = 64 — 289 + 34CD — CD2

AD2 = AC2 — CD2 = 225 — CD2

64 — 289 + 34CD — CD2 = 225 — CD2

-225 + 34CD = 225

34CD = 225 + 225 = 450

CD = 450/34 = 13,2

AD2 = AC2 — CD2 = 225 — 174,24 = 50.76

AD = √50,76 = 7,1