Construct a triangle MNP, whose perimeter is 15 cm and whose sides are in the ratio 2:3:4.

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.