Construct a triangle PQR in which PQ = 5.5 cm, PR = 6.2 cm and length of the perpendicular from P on QR is 4 cm.

We have been given two sides of a triangle and its perpendicular height.

Steps of construction are:

1. Draw a line segment XY long enough using a ruler.

2. Take a point M on XY.

3. Draw ZM ⊥ XY, with ZM sufficiently large.

To draw perpendicular ZM: With M as centre, draw a circle/semicircle of radius say 3 cm cutting the line XY at A and B on XY. Taking each A and B as centre one by one, draw an arc or circle of radius 2.8 cm (say). These arcs or circle should intersect the circle of centre M. The points at which they intersect, draw two more arcs or circles of radius 2.5 cm. Let the point at which these arcs or circles intersect be Z. Join MZ.

4. With M as centre and radius 4 cm, draw a circle or arc cutting the line segment ZM at P.

5. With P as centre and radii 5.5 cm and 6.2 cm, draw circles or arcs cutting XY at Q and R respectively.

6. Join PQ and PR.

Thus, PQR is the required triangle.