Construct a triangle ABC, whose perimeter is 13 cm and whose sides are in the ratio 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 = 13 cm.

2. Draw a ray XZ, making an acute angle with XY and drawn in the downward direction. An acute angle is an angle less than right angle (less than 90°). Use the protractor to measure the acute angle.

Here, ∠YXZ < 90° obviously.

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 a circle or semicircle or 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 circle or semicircle or arc cutting the previous arc at A.

Keep one end of the compass fixed at C, and then draw a fine circle or arc with it.

8. Finally, join AB and AC.

Thus, ABC is the required triangle.