Respuestas
Respuesta:
1. 42 cm 2. 48 cm 3. 30 cm 4. 20 cm
Explicación paso a paso:
1. Triángulo rectángulo: (x + 7) + (x + 6) + (x + 8)
3x = 6 + 7 + 8
3x = 7 + 7 + 7
x = 21 / 3 = 7
Perímetro = 7 + 7 + 7 + 6 + 7 + 8 = 21 + 13 + 8 = 29 + 13 = 42 cm.
2. Cuadrado: y + 6 (4 lados)
4(y + 6) = 0
(y + 6) + (y + 6) + (y + 6) + (y + 6) = 0
4y = 6 + 6 + 6 + 6
4y = 12 + 12
y = 24/4 = 6
Perímetro = 4(6 + 6) = 4*12 = 48 cm.
3. Trapecio: 5m + 7 (base), 3m + 4 (la de arriba), 4m + 2 (cada lado).
(5m + 7) + (3m + 4) + 2(4m + 2) = 0
5m + 3m + 8m + 4 = 7 + 4
16m = 11 + 4
m = 15/16
Perímetro = (5*15/16 + 7) + (3*15/16 + 4) + 2*(4*15/16 + 2) =
75/16 + 7/1 + 45/16 + 4/1 + 2*(60/16 + 2/1) =
75/16 + 112/16 + 45/16 + 64/16 + 2*(60/16 + 32/16) =
187/16 + 109/16 + 2*(92/16) =
296/16 + 184/16 = 480/16 = 30 cm.
4. Pentágono: 4w + 2 (5 lados)
(4w + 2) + (4w + 2) + (4w + 2) + (4w + 2) + (4w + 2) =
4w + 4w + 4w + 4w + 4w = 2 + 2 + 2 + 2 + 2
8w + 8w + 4w = 10
20w = 10
w = 10/20 = 1/2
Perímetro = (4*1/2 + 2) + (4*1/2 + 2) + (4*1/2 + 2) + (4*1/2 + 2) + (4*1/2 + 2) =
5(4/2 + 2/1) =
5( 4/2 + 4/2 ) =
5*8/2 = 40/2 = 20 cm.