1 Answer

Carrots · Answer 1 · 2019-09-30T02:46:40+0000

The formula of a diameter d of a square with side a:

$d=a\sqrt2$

Substitute
$d=\sqrt6\ mm$ :

$a\sqrt2=\sqrt6$ multiply both sides by
$\sqrt2$

2a=√(12) used
$√(a)\cdot√(a)=a$ and
$√(a\cdot b)=√(a)\cdot√(b)$

$2a=√(4\cdot3)$ use
$√(a\cdot b)=√(a)\cdot√(b)$

$2a=\sqrt4\cdot\sqrt3$

$2a=2\sqrt3$ divide both sides by 2

$a=\sqrt3\ mm$

The perimeter:
P=4a

Substitute:

$P=4\sqrt3\ mm$

Other method.

Use the Pythagorean theorem:

$a^2+a^2=(\sqrt6)^2$ use

2a^2=6 divide both sides by 2

$a^2=3\to a=\sqrt3\ mm$

$P=4a\to P=4\sqrt3\ mm$

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