Առաջադրանքներ՝ 366-372

ա) a = 6
b = 8
c = ?

c² = a² + b² = 36 + 64 = 100
√100 = 10

բ) a = 5
b = 12

c² = a² + b² = 25 + 144 = 169
√ 169 = 13

գ) a = 3/7
b = 4/7

c² = a² + b² = 9/49 + 16/49 = 25/49
√ 25/49 = 5/49

դ) a = 1
b = √ 3

c² = a² + b² = 1 + 3 = 4
√4 = 2

ա) a = 12
c = 13

b² = c² — a² = 169 — 144 = 25

√25 = 5

բ) a = 9
c = 15

b² = c² — a² = 225 — 81 = 144

√144 = 12

գ) a = 2
c = √5

b² = c² — a² = 5 — 4 = 1

√1 = 1

դ) a = 6
c = 2b

b² = c² — a² = 4b² — 36

b² — 4b² = -36

-3b² = -36

b² = 12

√12 = 2 √3

a = ?

b = c/2

c² = a² + b² = a² + c²/4

c² — c²/4 = a²

(4c² — c²)/4 = a²

3c²/4 = a²

a = √3c²/4 = c√3/2

ա)

AD = ?

BC² = AC² — AB² = 169 — 25 = 144

√144 = 12

AD = BC = 12

բ)

BC = ?

AD² = AC² — CD² = 6,25 — 2,25 = 4

√4 = 2

BC = AD = 2

գ)

CD = ?

CD² = BD² — BC² = 289 — 225 = 64

√64 = 8

BH = ?

AH = HC = 16:2 = 8

BH² = AB² — AH² = 289 — 64 = 225

√225 = 15

ա)

BH = ?

AH = HC = 6:2 = 3

BH² = BC² — AH² = 36 — 9 = 27

√27 = 3√3

բ)

AB = BC = AC = ?

AB² = BH² + AH² = BH² + AB²/4 = 16 + AB²/4

AB² — AB²/4 = 16

(4AB²-AB²)/4 = 16

3AB²/4 = 16

3AB² = 64

AB² = 64/3

√64/3 = 8/√3

AB = BC = CD = AD = ?

AC² = AB² + BC² = AB² + AB² = 2AB²

400 = 2AB²

AB² = 400/2 = 200

√200 = 10√2

AB = BC = CD = AD = 10√2