# Construct a

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 A on XY.

3. Draw ZA XY, with ZA sufficiently large.

To draw perpendicular ZA: With A as centre, draw a circle/semicircle of radius say 3 cm cutting the line XY at B and C on XY. Taking B and C as centre, draw an arc or circle of radius 2.5 cm (say). These arcs or circle should intersect the circle of centre A. The points at which they intersect, draw two more arcs or circles of radius 3.2 cm. Let the point at which these arcs or circles intersect be Z. Join AZ.

4. With A as centre and radius 3.8 cm, draw a circle or arc cutting the line segment ZA at M.

5. With M as centre and radii 4.5 cm and 5.2 cm, draw circles or arcs cutting XY at N and P respectively.

6. Join MN and MP.

Thus, MNP is the required triangle.

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