Respuestas
PROBLEMA 1
P = 142 m
b = 4x - 5
h = 3x + 6
P = 2b + 2h
142 = 2(4x - 5) + 2(3x + 6)
142 = 8x - 10 + 6x + 12
142 + 10 - 12 = 8x + 6x
140 = 10x
x = 140/10
x = 10
b = 4x - 5
b = 4(10) - 5
b = 40 - 5
b = 35
h = 3x + 6
h = 3(10) + 6
h = 30 + 6
h = 36
A = bh
A = 35(36)
A = 1260 m²
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PROBLEMA 2
h = x
b = x + 6
A = 280 m²
A = bh
280 = (x)(x + 6)
280 = x² + 6x
x² + 6x - 280 = 0
a = 1
b = 6
c = -280
{-b ± √[(b)² - 4ac]} / 2a
{-(6) ± √[(6)² - 4(1)(-280)]} / 2(1)
{-6 ± √[36 + 1120]} / 2
{-6 ± √[1156]} / 2
{-6 ± 34} / 2
x1 = (-6 + 34) / 2
x1 = 28 / 2
x1 = 14
x2 = (-6 - 34) / 2
x2 = -40 / 2
x2 = -20 --> ya que hablamos de medidas físicas, la respuesta no puede ser negativa.
b = x
b = 14 m
h = x + 6
h = 14 + 6
h = 20 m
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PROBLEMA 3
Kg de almedra = x
Kg de nuez = y
5x + 4y = 2120
8x + 6y = 3280
5x = 2120 - 4y
x = (2120 - 4y) / 5
8x = 3280 - 6y
x = (3280 - 6y) / 8
x = x
(2120 - 4y) / 5 = (3280 - 6y) / 8
(2120 - 4y)(8) = (3280 - 6y)(5)
16,960 - 32y = 16,400 - 30y
16960 - 16400 = -30y + 32y
560 = 2y
y = 560 / 2
y = 280 el kg de nuez
5x + 4y = 2120
5x + 4(280) = 2120
5x + 1120 = 2120
5x = 2120 - 1120
5x = 1000
x = 1000 / 5
x = 200 el kg de almendra
** comprobación **
8x + 6y = 3280
8(200) + 6(280) = 3280
1600 + 1680 = 3280
3280 = 3280
la respuesta es correcta :)