Question

Ayúdenme con este ejercicio de Semejanza llevo horas intentándolo!

Answer 1

Respuesta:

Triangulo ABC:

AB = 9

BC = 8

AC = 14

Triangulo MNP:

MN = 27

MP = 24

NP = 42

Explicación paso a paso:

Del Gráfico:

El Triangulo ABC es semejante al Triangulo MNP:

AB / MN = BC / MP

(x + 4) / (5x + 2) = (x + 3) / (5x - 1)

(5x - 1)(x + 4) = (5x + 2)(x + 3)

5x² + 20x - x - 4 = 5x² + 15x + 2x + 6

5x² + 19x - 4 = 5x² + 17x + 6

19x - 4 = 17x + 6

19x - 17x = 4 + 6

2x = 10

x = 5

Luego:

AB / MN = AC / NP

(x + 4) / (5x + 2) = (y + 5) / (5y - 3)

(5 + 4) / (5(5) + 2) = (y + 5) / (5y - 3)

9 / (25 + 2) = (y + 5) / (5y - 3)

9 / 27 = (y + 5) / (5y - 3)

1 / 3 = (y + 5) / (5y - 3)

(5y - 3) = 3(y + 5)

5y - 3 = 3y + 15

5y - 3y = 3 + 15

2y = 18

y = 9

Triangulo ABC:

AB = x + 4 = 5 + 4 = 9

BC = x + 3 = 5 + 3 = 8

AC = y + 5 = 9 + 5 = 14

Triangulo MNP:

MN = 5x + 2 = 5(5) + 2 = 25 + 2 = 27

MP = 5x - 1 = 5(5) - 1 = 25 - 1 = 24

NP = 5y - 3 = 5(9) - 3 = 45 - 3 = 42