Construct a triangle whose perimeter is 12 cm and the ratio of their sides is 3:4:5.

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 = 12 cm.

2. Draw a ray XZ, making an acute angle with XY and drawn in the downward direction. An acute angle is an angle smaller than a right angle (it is less than 90 degrees).

Clearly, the ∠YXZ < 90°.

3. From X, locate (3 + 4 + 5) = 12 points at equal distances along XZ.

4. Mark points L, M, N on XZ such that XL = 3 parts, LM = 4 parts and MN = 5 parts.

5. Now, join NY. Through L and M, draw LB ∥ NY and MC ∥ NY, intersecting XY at B and C respectively.

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

7. With C as centre and CY as radius, draw another arc cutting the previous arc at A. Keep one end of the compass at C and the other at Y, and then draw a fine circle or arc with it.

8. Finally, join AB and AC.

Thus, ABC is the required triangle.