Question

Jaya drew an incircle of a square. That circle is also circumscribe an equilateral triangle of
which each length of side is 4V 3 cm. Let us write by calculating the length of diagonal of
square.​

Answer 1

Hello mate!!!

Your answer with step by step explanation is mentioned below:

Step by step explanation:

First we will calculate circumradius of equilateral triangle which is given by

$\frac{s}{ \sqrt{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: where \: \: \: \:s \: \: \: \: is \: side \: of \: equilateral \: triangle$

Substituting the value of s= 4√3, we get:

$= \frac{4 \sqrt{3} }{ \sqrt{3} } \: cm$

$= 4 \: cm$

Which is inradius (i) of square

Now, Lets calculate the side of square which is given by:

$2i \: \: \: \: \: \: \: \: where \: \: \: \: i \: \: \: \: \: is \: inradius \: of \: the \: square$

Substituting the value of i = 4 cm, we get:

$2 \times 4 \: cm$

$= 8 \: cm$

and that is the side (a) of the square

Now the final step that is calculating the diagonal of square which is given by the formula:

$a \sqrt{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: where \: \: \: \: \: a \: \: \: \: is \: \: the \: side \: of \: the \: square$

Substituting the value of a=8 cm, we get:

$= 8 \sqrt{2} \: cm$

$and \: that \: is \: the \: answer$

Hope it helps,

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