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Dmitry_Shevchenko [17]
3 years ago
5

A regular hexagon and an equilateral triangle have equal perimeters. what is the ratio of the area of the hexagon to the area of

the triangle? express your answer as a common fraction.
Mathematics
1 answer:
Tresset [83]3 years ago
8 0
In this item, we let the perimeter of both polygons be P. The lengths of each side are calculated below.

Hexagon:   s = (p/6) = p/6
Triangle:     s = (p/3) = p/3

The areas of each polygon are also calculated below. It is noted that the polygons are regular (meaning, each side and angle are equal).

Area of Hexagon:    A = 3√3/2 a²
 Substituting the known values,
                     A = 3√3/2(P/6)²
Simplifying,
                      A = √3/24P²

For the triangle,
              A = √3/4a²

Substituting,
                A = √3/4 (P/3)²
Simplifying,
               A = √3/36P²

The ratio is equal to:
              ratio = (√3/24P²) / (√3/36P²)
              <em>  ratio = 3/2</em>
<em>                    ratio = 1.5</em>
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The length of the terrarium is 14.5 inches and the width is 7 inches. what is the height of the terrarium?
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Law Incorporation [45]

Answer:

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  2. y = 25 + 0.9x
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Step-by-step explanation:

1. 10% of $50 is $5, so the purchases would come to $50 -5 = $45. Added to the $25 membership fee, the total cost for the year would be

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2. The member pays $25 even if no purchases are made. Then any purchases are 100% - 10% = 90% of the marked price. So, the total is ...

  y = 25 + 0.90x

3. $25 is 10% of $250, so that is the amount the member would have to purchase to break even on cost.

If you like, you can compare the cost without the membership (x) to the cost with the membership (25+.9x) and see where those costs are equal.

  x = 25 +0.9x . . . . . x is the spending level at which there is no advantage

  0.1x = 25 . . . . . . . . subtract 0.9x

  25/0.1 = x = 250 . . . divide by 0.1

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3 years ago
The shortest warmer was blue. The two longest warmers were pink.
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Answer:

8

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The shortest leg warmer:

4.5

The longest leg warmers:

6 and 6.5

6 + 6.5 = 12.5

12.5 - 4.5 = 8

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