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Answer :
Steps of construction:
1. Take a ray AX with initial point A. From AX, cut off AB = 4cm.
2. Taking A as centre and radius (= 4 cm), draw an arc of a circle, which intersects AX, say at a point B.
3. Taking B as centre and with the same radius as before, draw an arc intersecting the previously drawn arc, say at a point C.
4. Draw the ray AE passing through C.
5. Next, taking B as centre and radius (= 4 cm), draw an arc of a circle, which intersects AX, say at a point A.
6. Taking A as centre and with the same radius as in step 5, draw an arc intersecting the previously drawn arc, say at a point C.
7. Draw the ray BF passing through C. Then, ABC is the required triangle with gives side 4 cm.
Justification:
AB = BC ...(By construction)
AB = AC ...(By construction)
Thus, AB = BC = CA
Therefore, \(\triangle{ABC}\) is an equilateral triangle.
Hence, The construction is justified.