Question 557587
<br><font face="Tahoma">The longest line segment that can be drawn from any 2 points on a square,<br>

must naturally be a diagonal of a square.  No other possible line segment will be as long as any diagonal of the square.<br>

You can test this out with any ruler, and any true square.<br>

So, given a side of 9 cm, we can use the Pythagorean Theorem to find the length of the diagonal of the square.<br>

{{{a^2+b^2=c^2}}}<br>

{{{9^2+9^2=c^2}}}<br>

{{{81+81=c^2}}}<br>

{{{162=c^2}}}<br>

{{{sqrt(162)=c}}} or {{{-sqrt(162)=c}}}<br>

Since we are dealing with distances, we can discard the negative solution.<br>

{{{c=sqrt(162)}}}<br>

{{{c=sqrt(81*2)}}}<br>

{{{c=9*sqrt(2)}}}  which is the exact answer<br>

The longest line segment would be {{{9*sqrt(2)}}} cm.<br>

Alternatively, we can find an approximation for this answer:<br>

{{{c=12.73}}} cm<br>

Using the familiar rules of geometry, and recognizing that a square is cut into two 45-45-90 triangles by a diagonal,<br>

we could have immediately determined the length of the diagonal to be {{{9*sqrt(2)}}} cm long.<br>

But then we wouldn't have had the nice opportunity to use the Pythagorean Theorem!<br>

I hope this helps!  :)<br>

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