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ella [17]
3 years ago
10

A candy bar box is in the shape of a triangular prism. The volume of the box is 2,400 cubic centimeters. A triangular prism is s

hown with base of triangle labeled 16 cm, sides of triangles labeled 17 cm, and length of the box equal to 20 cm. Part A: What is the height of the base? Show your work. (5 points) Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)
Mathematics
1 answer:
Elena-2011 [213]3 years ago
8 0

Answer:

  A) 15 cm

  B) 1240 cm²

Step-by-step explanation:

Part A: The height of the triangular base can be found a couple of ways. One is to use the Pythagorean theorem.

The triangular base is isosceles, so the height, half its base (8 cm) and the long edge (17 cm) form a right triangle. The height is then found from ...

  17² = 8² + height²

  289 -64 = height² . . . . . subtract 64

  √225 = 15 = height . . . . take the square root

The height of the triangular base is 15 cm.

__

Part B: The volume of a prism is given by ...

  V = Bh

where B is the area of the base and h is the length ("heigh") of the prism. We can use this formula to find B, the area of each of the triangular bases of the prism.

  2400 cm³ = B·(20 cm)

  2400 cm³/(20 cm) = B = 120 cm² . . . . . area of one end of the prism

Now the lateral area of the prism is the product of its length (20 cm) and the perimeter of its base (17 cm + 17 cm + 16 cm). That area is ...

  lateral area = (20 cm)(50 cm) = 1000 cm²

Together with the areas of the two ends, we find the total area of the cardboard box to be ...

  total area = lateral area + 2×base area = 1000 cm² + 2×120 cm²

  total area = 1240 cm²

_____

Note that you can also find the <em>height of the base triangle</em> from the base area.

  A = (1/2)bh

  120 cm² = (1/2)(16 cm)h

  120 cm²/(8 cm) = <em>h = 15 cm</em>

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The total number of people at a football game was 5600. Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.
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1100 field-side tickets and 4500 end-zone tickets.

Step-by-step explanation:

Let x represent number of field side tickets and y represent number of end-zone tickets.

We have been given that the total number of people at a football game was 5600. We can represent this information in an equation as:

x+y=5600...(1)

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We are also told that Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.

Cost of x field side tickets would be 40x and cost of y end-zone tickets would be 20y.

The total amount of money received for the tickets was $134000. We can represent this information in an equation as:

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Upon substituting equation (1) in equation (2), we will get:

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