Geometry

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Complete the indirect proof.

Given: Rectangle JKLM has an area of 36 square centimeters. Side JK is at least 4 centimeters long.
Prove: KL<=9 centimeters

  • Geometry -

    Statements:
    Let
    p: A=36 ∧ JK≥4
    q: KL≤9

    Indirect proof (by contradiction):
    We try to establish:
    p->q
    i.e. if p is true, then q is true.

    We will assume that p is true and q is false, i.e.
    A=36, JK≥4, and that KL>9.

    Let JK=4+x : x≥0, and
    KL=9+y : y>0
    so
    A=JK*KL
    =(4+x)(9+y)
    =36+9x+4y+xy
    Since y>0, so A>36
    which cannot be true.
    Therefore the assumption of
    p and true and q is false is not valid (contradiction).
    Therefore when p is true, q is true, or
    p->q.
    or
    if A=36, and JK≥4 then KL≤9.

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