374, 375, 376

ա)

AC = 12սմ
BH = 8սմ
AB = BC = ?

S = 12 * 8/2 = 48սմ²

AH = HC = 12 : 2 = 6

AB2 = BH2 + AH2 = 64 + 36 = 100

√100 = 10

AB = BC = 10

բ)

AC = 18սմ
<B = 120սմ
AB = BC = ?

<ABH = <CBH = 60
<A = <B = 30
BH = x
AB = 2x
AH = HC = 18:2 = 9

AB2 = BH2 + AH2

4×2 = x2 + 81
4×2 — x2 = 81
3×2 = 81
x = 81/3
√81/3 = 9/√3

AB = 2 * 9/√3 = 6√3

S = (18 * 27√3)/2 = 243√3

գ)

AH = 7սմ
AB = BC = ?

BH = AH = 7սմ
BC = 2 * BH = 14սմ

S = 14*7/2 = 49սմ2

ա)

AH = ?

BC2 = AB2 + AC2 = 25 + 144 = 169
BC = √169 = 13

AH2 = AC2 — CH2 = AC2 — (BC — BH)2 = 144 — (13 — BH)2
AB2 — BH2 = 144 — (13 — BH)2
25 — BH2 = 144 — 169 — 26BH — BH2
25 + 169 — 144 = 26BH
50 = 26BH
BH = 50/26 = 25/13
AH2 = AB2 — BH2 = 25 — 625/169 = (25 * 169 — 625)/169 = 3600/169

AH = √3600/169 = 60/13

բ)

BC2 = AB2 + AC2 = 144 + 256 = 400
BC = √400 = 20

AH2 = AB2 — BH2 = 144 — BH2
AH2 = AC2 — CH2 = 256 — (BC — BH)2 = 256 — (13 — BH)2
144 — BH2 = 256 — 169 + 26BH — BH2
144 — 256 + 169 = 26BH
57 = 26BH
BH = 57/26
AH2 = AB2 — BH2 = 144 — (57/26)2 = 144 — 3249/676 = (144-676)/676 = (97344 — 3249)/676 = √94095/676 = 105/52

AH = HC = 12 : 2 = 6

BH2 = AB2 — AH2 = 100 — 36 = 64
BH = √64 = 8

AN2 = AB2 — BN2 = 100 — BN2
AN2 = AC2 — CN2 = 144 — (BC — BN)2 = 144 — (10 — BN)2

100 — BN2 = 144 — (10 — BN)2
100 — BN2 = 144 — (100 — 20BN + BN2)
100 — BN2 = 144 — 100 + 20BN — BN2

100 — 144 + 100 = 20BN
156 = 20BN

BN = 156/20 = 16/20

AN2 = AB2 — BN2 = 100 — 256/400 = (40000 — 256)/400 = 2484/25