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MWSiOUX

An isosceles trapezoid has an area of 21540 feet. What are the lengths of each base and the height?

  • one year ago
  • one year ago

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  1. pfenn1
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    What does the fact that it is an isosceles triangle tell you about the sides of the triangle?

    • one year ago
  2. MWSiOUX
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    They're the same.

    • one year ago
  3. pfenn1
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    Sorry, I meant isosceles trapezoid.|dw:1342964621092:dw|A trapezoid is a quadrilateral with exactly one pair of parallel sides. In a trapezoid the parallel sides are called bases. A pair of angles that share a base as a common side are called a pair of base angles. A trapezoid with the two non-parallel sides the same length is called an isosceles trapezoid. The base angles of an isosceles trapezoid are equal in measure.

    • one year ago
  4. pfenn1
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    The area is given by\[A = \frac12(a+b)h\]

    • one year ago
  5. pfenn1
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    Do you have enough information to solve this problem?

    • one year ago
  6. MWSiOUX
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    I'm not sure.

    • one year ago
  7. agentx5
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    I don't think you have enough information actually... The two figures below could potentially have the same area |dw:1342966291436:dw|

    • one year ago
  8. agentx5
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    In the same way that the can: |dw:1342966455204:dw|

    • one year ago
  9. MWSiOUX
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    That was all the information I was given. It's for an area of a playground.

    • one year ago
  10. agentx5
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    But you see what I mean with the rectangle right? What's 2m times 8m? 16m\(^2\) right?

    • one year ago
  11. MWSiOUX
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    Yes. What I'm doing now is using the formula for the area of a trapezoid (.5h(b1+b2)) and made b1 = h (to simplify things a bit).

    • one year ago
  12. MWSiOUX
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    And then I used a graph to see what points could fit the bases more realistically. I got b1 = h = 120 and b2 = 239.

    • one year ago
  13. MWSiOUX
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    Would that be an isosceles trapezoid then? How could I tell?

    • one year ago
  14. MWSiOUX
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    \[21540 = (1/2)b _{1}(b _{1}+b _{2})\] \[(43080-b _{1}^{2})/b _{1}=b _{2}\]

    • one year ago
  15. MWSiOUX
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    b1=120 and b2=239 happens to fit that.

    • one year ago
  16. agentx5
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    Whoa not so fast there... look: Prime factorization of your area: 21540 ft\(^2\) = 2 * 2 * 3 * 5 * 359 * ft * ft There's going to more than one correct, whole-unit answer! That's my point, you need a bit more information. 120 + 239 = 359 1/2 * (359) * 120 = 21540, correct! But... so is: 1/2 * (139 + 220) * 120 = 21540, also correct!

    • one year ago
  17. agentx5
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    http://mathworld.wolfram.com/IsoscelesTrapezoid.html

    • one year ago
  18. agentx5
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    As I said, more than one correct, whole # answer. Let roots also be include in options for answers, and you'll potentially get an unlimited set of correct answers. You need more information. If the goal was to find just one of them, then you're good. But there's more than one answer here. ;-)

    • one year ago
  19. MWSiOUX
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    Indeed. It's for a playground so I'd rather have a iso trap with more of a square inner area rather than a elongated, skinny inner area.

    • one year ago
  20. agentx5
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    If you want to find, whole number answers for these, you'll need to always write out prime factorizations as the first step. A calculus version of this problem would ask you to find the local minimum or maximum for something, or approaching a specific value (like if we needed the longest side to be no more than 200m)

    • one year ago
  21. agentx5
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    Make sense?

    • one year ago
  22. MWSiOUX
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    I was thinking about using the calculus approach but this is just for a college geometry course. So, I'm trying to think in a geometric aspect rather than a calculus aspect.

    • one year ago
  23. MWSiOUX
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    And yes, I understand. Thank you for your help!

    • one year ago
  24. agentx5
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    Ok this question got me thinking, I'm going to make a challenge question for the bored people who like mental puzzles from this original question :-D (don't worry I'll link it back @MWSiOUX )

    • one year ago
  25. MWSiOUX
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    Awesome!

    • one year ago
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