tmua.me Extreme Set B Paper 2 · Question 3 · ExamDay

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tmua.me Extreme Set B Paper 2 · Q3

Paper 2Logic & proofGeometry

Let $k\geq0$ . Consider the statements

S: $0\leq k<7+4\sqrt3$ .
T: For every triangle of positive area whose side lengths $a$ , $b$ and $c$ satisfy

$\displaystyle a>1,\qquad b>1,\qquad c>1,$

the three numbers

$\displaystyle a+\frac{k}{a},\qquad b+\frac{k}{b},\qquad c+\frac{k}{c}$

can also be used as the side lengths of a triangle of positive area.

Is S necessary and/or sufficient for T?

AS is neither necessary nor sufficient for T

BS is necessary but not sufficient for T

CS is sufficient but not necessary for T

DS is necessary and sufficient for T

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