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Math Help - Please help me to solve this problem.

  1. #1
    Junior Member
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    Please help me to solve this problem.

    In AB and BC legs of ABC triangle are points S and R, respectively, such that AS=3/7 of AB and BR=3/8 of BC. Find the area of SBR triangle if the area of ABC is 126 sq.cm
    Last edited by blertta; October 27th 2007 at 12:16 AM. Reason: I am sorry.English is not my native lanuage.
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  2. #2
    MHF Contributor
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    Okay, I understand what you mean. (English is not my native language also.)

    You are saying,
    In AB and BC (not CD) legs of ABC triangle are points S and R, respectively, such that AS=3/7 of AB and BR=3/8 of BC. Find the area of SBR triangle if the area of ABC is 126 sq.cm.

    Since only sides are given with values, and the area of triangle ABC, only, and since triangles ABC and SBR have the same angle B, then we will use the formula for the area of any triangle,
    A = (1/2)ab*sin(theta)
    where
    theta is the angle between sides a and b.

    In triangle ABC,
    Let x = AB
    And y = BC
    So,
    Area of ABC = (1/2)(x)(y)sinB = 126
    xy*sinB = 252 ------------------------(i)

    ----------------------------------
    In triangle SBR,

    SB = (4/7) of AB because AS is (3/7) of AB
    So,
    SB = (4/7)x

    BR = (3/8) of BC
    BR = (3/8)y

    Area of SBR
    = (1/2)[(4/7)x][(3/8)y]sinB
    = [12/(2*56)](xy)sinB
    = (3/28)(xy)sinB

    Substitute into that the xy*sinB = 252,

    = (3/28)(252)
    = 27 sq.cm ----------------------answer.
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  3. #3
    Super Member

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    Lexington, MA (USA)
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    Hello, blertta!

    In AB and CD legs of ABC triangle are picked up two points S and R
    where: . AS\,=\,\frac{3}{7}(AB),\;BR\,=\,\frac{3}{8}(BC)

    Find the area of \Delta SBR if the area of \Delta ABC = 126 cm².
    Code:
                    C
                    *
                   *  *
              5/8 *     *
                 *        *
              R o           *
               * **           *
              *   *   *         *
         3/8 *     *      *       *
            *       *         *     *
           *         *            *   *
        B * * * * * * o * * * * * * * * * A
              4/7     S        3/7

    \Delta SBR's height is \frac{3}{8} of \Delta ABC's height.

    \Delta SBR's base is \frac{4}{7} of \Delta ABC's base.

    Therefore: . \Delta SBR \;=\;\left(\frac{3}{8}\right)\left(\frac{4}{7}\rig  ht)(126) \;=\;27\text{ cm}^2

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