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Math Help - area of triangle

  1. #1
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    area of triangle

    The dimensions of a triangle are 13, 13, and 24. What is the area in square units of this triangle?

    A) 30 B) 60 C) 90 D) 156 E) 312
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  2. #2
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    Hello, sri340!

    Obviously, you didn't make a sketch . . .


    The dimensions of a triangle are 13, 13, and 24.
    What is the area of this triangle?

    . . A) 30 . . B) 60 . . C) 90 . . D) 156 . . E) 312
    Code:
                          *
                13    *   |   *    13
                  *       |h      *
              *           |           *
          * - - - - - - - * - - - - - - - *
                  12             12

    The base of this triangle is 24.

    Can you find the height h ?

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  3. #3
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    Quote Originally Posted by sri340 View Post
    The dimensions of a triangle are 13, 13, and 24. What is the area in square units of this triangle?

    A) 30 B) 60 C) 90 D) 156 E) 312
    In a test situation, a sketch as Soroban suggested would have helped immensely, & you probably could have solved it immediately.

    Alternatively, use could use Heron's formula

    Area = \sqrt{s(s-a)(s-b)(s-c)}

    s =  \dfrac{ 13+13+24 }{2} = 25

    Area = \sqrt{25 (25-13)(25-13)(25-24)}

    Area = \sqrt{25 \cdot 12 \cdot 12 \cdot 1 }

    .You should not require a calculator to extract that square root.
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  4. #4
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    That's because each half of Soroban's picture is a "5-12-13" right triangle!
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  5. #5
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    Quote Originally Posted by sri340 View Post
    The dimensions of a triangle are 13, 13, and 24. What is the area in square units of this triangle?

    A) 30 B) 60 C) 90 D) 156 E) 312
    the triangle is isosceles with base = 24 units
    dividing it into two congruent right angled triangles, each has hypotenuse = 13 and the base = 24/2 = 12
    the other side (height) = \sqrt{13^2 - 12^2} = 5
    so the area is 24 x 5 / 2 = 60 sq units
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