Question 1129618: Explain how to construct a line segment with length square root of 13 cm? Found 2 solutions by josmiceli, ikleyn:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Is this with compass and straightedge alone?
If so, then:
(1) draw a straight line
(2) construct a perpendicular to the line at point A
(3) bisect one of the 90 degree angles formed
(4) lay out 13 units on this bisector ( any units )
Call the end of this line segment B
(5) drop a perpendicular from B
to the original line. call the intersection C
(6) the line segment AC is units long
Therefore, is the length of the hypotenuse of the right angled triangle with the legs of 3 and 2 centimeters long.
So, with a liner and a compass the construction is as follows.
Draw a straight line.
From the point A on the line, construct the segment AB on the line of the length 3 centimeters.
Construct the perpendicular line to the straight line AB at the point B.
On the perpendicular, construct the segment BC of the length 2 cm.
Connect the point A and C by the liner.
The segment AC is what you need.
The referred lessons are the part of this online textbook under the topic "Geometric constructions using a compass and a ruler. Basic operations".
Save the link to this online textbook together with its description
Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson
to your archive and use it when it is needed.
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Notice that the construction algorithm, given in the post by @josmicely, gives you the segment of the length ,
which is totally different from what the problem does require.
