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Question Number 179440 by mr W last updated on 29/Oct/22

Commented by mr W last updated on 29/Oct/22

$$findthelargestequilateraltriangle$$$$whichcanbeplacedinsideasquare$$$$withsidelength1.$$

Commented by Beginner last updated on 29/Oct/22

$$Approx1.0353$$

Commented by nikif99 last updated on 29/Oct/22

$$x^2=a^2+1^2=b^2+1^2\Rightarrow a=b\Rightarrow \vartheta =15°\Rightarrow$$$$a=\left(\tan 15\right)/1=2-\sqrt{3}$$$$x=\sqrt{{(2-\sqrt{3})}^2+1}=2\sqrt{2-\sqrt{3}}=1.0353approx.$$

Commented by nikif99 last updated on 29/Oct/22

Commented by mr W last updated on 29/Oct/22

$$thankssirs!$$

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