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Math Help - [SOLVED] math b - triangles

  1. #1
    ThebrightOne
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    [SOLVED] math b - triangles

    hi I'm new to the forum and not sure where to post. I just have a few questions that i need help answering.


    -Find the indicated length for each equilateral triangle with given lengths..

    altitude 3 square root 3; side? and side 12; altitude ?

    -A boy 6 feet tall casts a shadow 15 feet long. at the same time a tree casts a shadow of length 50 feet. what is the height, in feet, of the tree?

    -The three sides of a triangle measure 4, 8 and 9. find the length of the longest side of a similar triangle whose perimeter is 63.

    thank you in advance.


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  2. #2
    Senior Member DivideBy0's Avatar
    Joined
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    From
    Melbourne, Australia
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    Quote Originally Posted by ThebrightOne View Post
    hi I'm new to the forum and not sure where to post. I just have a few questions that i need help answering.


    -Find the indicated length for each equilateral triangle with given lengths..

    altitude 3 square root 3; side? and side 12; altitude ?

    -A boy 6 feet tall casts a shadow 15 feet long. at the same time a tree casts a shadow of length 50 feet. what is the height, in feet, of the tree?

    -The three sides of a triangle measure 4, 8 and 9. find the length of the longest side of a similar triangle whose perimeter is 63.

    thank you in advance.
    I've attached images for questions 1, 2, and 3

    1. In an equilateral triangle the altitude bisects a side (divides it in 2), so if x is the length of the side, by pythagoras we have:

    (3\sqrt{3})^2 + \left(\frac{x}{2}\right)^2 = x^2

    27+\frac{x^2}{4}=x^2

    108 + x^2 = 4x^2

    3x^2 = 108

    x^2= 36

    x = 6 (only the positive root because length is positive)

    2. Let a be the altitude:

    a^2+\left(\frac{12}{2}\right)^2 =12^2

    a^2 + 36 = 144

    a^2 = 108

    a = \sqrt{108}=6\sqrt{3}

    3. Let x be the height of the tree. Using similar triangles,

    x:6 = 50:15

    \frac{x}{6}=\frac{50}{15}

    x = 20

    4. If the triangle is similar, then the sides must be in proportion with each other, but they can all be enlarged by a factor k.

    So by equating the sum of the sides of the enlarged triangle with its perimeter:

    4k + 8k + 9k = 63

    k = 3

    So the factor is 3, and hence the largest side is 9k = 9(3) = 27
    Attached Thumbnails Attached Thumbnails [SOLVED] math b - triangles-similar.jpg   [SOLVED] math b - triangles-equi.jpg  
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