Question

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

Answer 1

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.