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Math Help - SAT question

  1. #1
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    SAT question

    3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?
    I 24
    II 20
    III 5
    A. I only
    B. II only
    C. III only
    D. II and III only
    E. I, II and III


    the correct answer is D i and get II 20 but not III 5

    sorry repost i put it in the wrong section earlier.
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  2. #2
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    Re: SAT question

    Quote Originally Posted by zambo34 View Post
    3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?
    I 24
    II 20
    III 5
    A. I only
    B. II only
    C. III only
    D. II and III only
    E. I, II and III


    the correct answer is D i and get II 20 but not III 5

    sorry repost i put it in the wrong section earlier.
    Actually the area of the triangle can be 20 as it's maximum and 0 at it's minimum.

    In the attachment you can see a triangle with it's base of 5 and it's height of 2. Thus it's area has the value 5.
    Attached Thumbnails Attached Thumbnails SAT question-dreieckflist5.png  
    Thanks from HallsofIvy and zambo34
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  3. #3
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    Re: SAT question

    Another way to think of it: Let \theta be the angle between the two sides of lengths 8 and 5. The area of the triangle is \frac{1}{2}*8*5*\sin \theta = 20 \sin \theta


    Since \sin \theta ranges between 0 and 1 (for 0 \le \theta \le \pi), the area can range from 0 to 20. The correct answer is D.


    Note: You don't need​ trig on the SAT, but you can definitely use it.
    Last edited by richard1234; June 26th 2012 at 12:04 PM.
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