Given a length of 1 construct a triangle using only a compas

Given a length of 1, construct a triangle using only a compass whose perimeter is a multiple
of 6. Explain the steps in your construction and how you know
it works

Solution

Since we have given the length of 1 and we have to create a triangle using only a compass whose perimeter is a multiple.

Step 1 -- First we draw a line of length 1 and then we again use the length of 1 to make it length of 2. Let we name it by AB.

Step 2 -- Now we draw a semi-arc of a random radius at one end of this line, let say at A. then we cut an another arc from the point where is meets AB to the semi-arc. this cut makes an angle of 60 degree.

Step 3 -- Now again we use length 1 and join the length 1 to A going through the arc and along with it, we join another 1 unit length line.

Step 4 -- Let we name C to the other end of the line drawn in step 3.

Step 5 -- Now we repeat same process from end B also.

Step 6 -- Now it automatically intersects at C.

And we are ready with an equailateral triangle of perimeter = 6