Construct a triangle PQR, whose perimeter is 14 cm and whose sides are in the ratio 2:4:5.

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 = 14 cm.

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

Here, ∠YXZ < 90° obviously.

3. From X, locate (2 + 4 + 5) = 11 points at equal distances along XZ.

4. Mark points L, M, N on XZ such that XL = 2 parts, LM = 4 parts and MN = 5 parts.

5. Now, join NY. Through L and M, draw LQ ∥ NY and MR ∥ NY, intersecting XY at Q and R respectively.

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

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

8. Finally, join PQ and PR.

Thus, PQR is the required triangle.