407, 408, 419, 420, 421

P = 42

P = (x + y) * 2 = 42

(x + y) = 21

S = 4x

S = 5y

{4x = 5y
{x + y = 21

x = 21 — y

4 (21 — y) = 5y

84 — 4y = 5y

84 = 9y

4 = 84/9

S = 5 * 84/9 = 420/9 = 140/3

S = 24սմ²

FE = 2 + 2 = 4

BH = FE = 4

BC = AD = 24 : 4 = 6

GN = 3 + 3 = 6

BC = AD = GN = 6

BH = 24 : 6 = 4

P = 6 + 6 + 4 + 4 = 20սմ²

ա)

AB = BC = 20

<A = <C = 30^o

30^o դիմաց ընկած կողմը հավասար է ներքնաձիգի կեսին, այսինքն՝

BH = AB : 2 = 20 : 2 = 10

AH2 = AB2 — BH2 = 400 — 100 = 300

AH = √300 = 10√3

AC = AH * 2 = 10√3 * 2 = 20√3

S = 20√3 * 10 / 2 = 100√3սմ²

բ)

CH = 6

<ACH = 45^o

<A = 180 — (90 + 45) = 45^o

△ACH-ը հավասարասրուն է
HC = AH = 6

BA = AH * 2 = 6 * 2 = 12

S = 12 * 6 / 2 = 36սմ²

BC = 34

AN = 25

NC = 15

AC = AN + NC = 35

BM = MC = 34 : 2 = 17

MN2 = MC2 — NC2 = 289 — 225 = 64

MN = √64 = 8

BH = MN * 2 = 8 * 2 = 16

S = 35 * 16 / 2 = 280սմ²

BH2 = AB2 — AH2 = 25 — (AC — CH)² = 25 — (12 — CH)² = 25 — 144 + 24CH — CH² = -119 + 24CH — CH²

BH2 = BC2 — CH2 = 169 — CH2

-119 + 24CH — CH² = 169 — CH²

24CH = 169 + 119 = 288

CH = 288/24 = 12