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August 23, 2014

August 23, 2014

Posted by **chica** on Thursday, November 18, 2010 at 10:15pm.

Given: Rectangle JKLM has an area of 36 square centimeters. Side JK is at least 4 centimeters long.

Prove: KL<=9 centimeters

- Geometry -
**MathMate**, Friday, November 19, 2010 at 1:07pmStatements:

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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