Answer :

We are given with perimeter of triangle and ratio of its sides. We need to construct a triangle using the given information.

Steps of construction:


1. Draw a line segment using ruler and locate points X and Y such that XY = 15 cm.



2. Draw a ray XZ, making an acute angle with XY and drawn in the downward direction.



3. From X, locate (2 + 3 + 4) = 9 points at equal distances along XZ.



4. Mark points A, B, C on XZ such that XA = 2 parts, AB = 3 parts and BC = 4 parts.



5. Now, join CY. Through A and B, draw AN CY and BP CY, intersecting XY at N and P respectively.



6. With N as centre and NX as radius, draw a circle or semicircle or an arc. Keep one end of the compass fixed at N, and then draw a fine circle or arc with it.



7. With P as centre and PY as radius, draw another circle or arc cutting the previous arc at M. Keep one end of the compass fixed at P, and then draw a fine circle or arc with it.



8. Finally, join MN and MP.



Thus, MNP is the required triangle.


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