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Klio2033 [76]
3 years ago
9

En una hoja de papel cuyo perímetro es de 96 centímetros, se quiere imprimir un volante de manera que el área impresa sea un rec

tángulo cuyo largo mida el doble del ancho, el margen superior mida 3 centímetros, el izquierdo 5 centímetros y los márgenes inferior y derecho midan 2 centímetros cada uno. ¿Cuál es el perímetro de la región impresa?, ¿cuál es el área?
Mathematics
1 answer:
elixir [45]3 years ago
7 0

Answer:

El perímetro de la región impresa es 72 cm y su área es 288 cm².  

Step-by-step explanation:

1. Tenemos el perímetro de la hoja de papel:

P₁ = 96 cm = 2l₁ + 2a₁  (1)  

Como sabemos el margen superior, inferior, izquierdo y derecho podemos encontrar la relación entre el largo y ancho del rectángulo interno (región impresa) con el largo (l) y ancho (a) del rectángulo externo (hoja de papel):      

l_{2} = l_{1} - (m_{s} + m_{i}) = l_{1} - (3 cm + 2 cm) = l_{1} - 5 cm  (2)            

a_{2} = a_{1} - (m_{d} + m_{iz}) = a_{1} - (2 cm + 5 cm) = a_{1} - 7 cm   (3)    

El perímetro del rectángulo interno es:

P_{2} = 2l_{2} + 2a_{2}    (4)

Introduciendo la ecuación (2) y (3) en (4):

P_{2} = 2l_{2} + 2a_{2} = 2(l_{1} - 5 cm) + 2(a_{1} - 7 cm) = 2l_{1} + 2a_{1} - 10 cm - 14 cm = 96 cm - 24 cm = 72 cm  

Por lo tanto el perímetro del rectángulo interno (región impresa) es 72 cm.

 

2. Ahora para encontrar el área rectángulo interno debemos encontrar el largo y ancho del mismo, sabiendo que:

l_{2} = 2a_{2}     (5)

Introduciendo (5) en (4):

P_{2} = 2l_{2} + 2a_{2} = 2*2a_{2} + 2a_{2} = 6a_{2}

a_{2} = \frac{P_{2}}{6} = \frac{72 cm}{6} = 12 cm

l_{2} = 2a_{2} = 2*12 cm = 24 cm

Entonces el área es:

A_{2} = l_{2}*a_{2} = 12 cm*24 cm = 288 cm^{2}

Por lo tanto el área del rectágulo interno (región impresa) es 288 cm².      

Espero que te sea de utilidad!  

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Answer:

x + Y = 39 or x = 39-y

20x + 50y = 1.40

20 (39 - y) + 50y = 11.40

7.80 - 20y + 50y = 11.40

30y = 11.40 - 7.80

30y = 3.60

y = 3.60/30

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x = 39 - 12 = 27 20p coins were collected.

Proof:

20*27 + 50*12 = 11.40

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11.40 = 11.40

I hope it helps.

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If we know the concepts of transformations and <em>horizontal</em> translation and that f(x) = √x and k = - 2, then the <em>transformed</em> function is g(x) = √(x + 2).

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This kind of transformation is defined by the following expression:

g(x) = f(x - k)     (1)

Where k represents a <em>rightward</em> translation for k > 0.

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2 years ago
Farmers Bob ,Joe and Larry sold apples at the farmers market .Bob sold 86 apples .Joe sold 12 times as many as Bob .Larry sold h
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Answer:

Altogether they sell <u>1634</u> apples.

Step-by-step explanation:

GIven:

Bob, Joe and Larry sold apples at the farmers market.

<u><em>Bob sold 86 apples. </em></u>

<u><em>Joe sold 12 times as many as Bob. </em></u>

<u><em>Larry sold half as many apples as Joe. </em></u>

Now, to find the total apples Bob, Joe and Larry they all sell together.

<u>Number of apples Bob sold</u> = 86.

<u>Number of apples Joe sold</u> = 12 times of 86.

=12\times 86\\\\=1032.

<u>Number of apples Larry sold</u> = \frac{1}{2}\ of\ 1032

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Now, to get the apples they sell altogether we add the number of apples sold by Bob, by Joe and by Larry:

86+1032+516

=1634.

Therefore, altogether they sell 1634 apples.

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