Question

1) Determine o valor de x nas imagens abaixo

Answer 1

Usando o Teorema de Tales, temos:  

1. a) x / 16 = 3 / 12

12 * x = 16 * 3

12x = 48

x = 48/12

x = 4

b) 6 / 9 = 4 / x

6 * x = 9 * 4

6x = 36

x = 36/6

x = 6

c) 12,8 / 16 = x / 13

12,8 * x = 16 * 13

12,8x =  208

x = 208/12,8

x = 16,25

d) 2 / 8 = 3 / x

2 * x = 8 * 3

2x = 24

x = 24/2

x = 12

e) 5 / x = 4 / 2

4 * x = 5 * 2

4x = 10

x = 10/4

x = 2,5

2,5 / y = 2 / 8

2 * y = 8 * 2,5

2y = 20

y = 20/2

y = 10

f) 3x / 4x - 7 = 5 / 2

3x * 2 = 5 * (4x - 7)

6x = 20x - 35

20x - 6x = 35

14x = 35

x = 35/14

x = 2,5

g) c / 15 = 16 / 12

12 * c = 15 * 16

12c = 240

c = 240/12

c = 20

18 / a = 20 / 15

15 * a = 20 * 18

15a = 360

a = 360/15

a = 24

15 / d = 12 / 20

12 * d = 20 * 15

12d = 300

d = 300/12

d = 25

24 / b = 15 / 25

15 * b = 25 * 24

15b = 600

b = 600/15

b = 40

2. x + 2 / 15  =  x / 10

15 * x = 10 * (x + 2)

15x = 10x + 20

15x - 10x = 20

5x = 20

x = 20/5

x = 4

A medida de QR é 6 cm.

Espero ter ajudado, bons estudos!