Question

Given a unit segment, construct a segment whose length is ✓3.

Answer 1

To construct a segment whose length is √3 given a unit segment, we can use the concept of similar triangles.

Step-by-step explanation:

To construct a segment whose length is √3 (square root of 3) given a unit segment, we can use the concept of similar triangles. Suppose we have a segment AB of length 1 unit. We can construct a right triangle ABC, where angle ABC is 90 degrees and AC is the segment we want to construct.

Since triangles ABC and ADE (where DE is parallel to BC) are similar, we can set up a proportion:

AB/DE = AC/BC

Substituting the known values, we get:

1/1 = √3/BC

Simplifying, we find that BC = √3. Therefore, we have constructed a segment whose length is √3.