SOLUTION: Explain how to construct a line segment with length square root of 13 cm?

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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

Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

13 = 9 + 4 = + .

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.

Solved.

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On basic operations in construction problems with a liner and a compass, see the lessons
    - HOW TO bisect a segment using a compass and a ruler
    - HOW TO bisect an angle using a compass and a ruler
    - HOW TO construct a triangle using a compass and a ruler
in this site.

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Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

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.



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