Question

Construct a parallelogram ABCD, when AB = 5 cm, BC = 6.2 cm and altitude on AB = 3 cm.

Answer 1

Given:

AB = 5 cm, BC = 6.2 cm and the altitude on AB = 3 cm.

Construct parallelogram ABCD.

Steps of construction:

1. Draw the base AB: Draw a line segment AB = 5 cm.
2. Construct the altitude on AB: At point A, draw a perpendicular line to AB. From A, cut off a length of 3 cm along this perpendicular line and mark this point as P this represents the altitude height.
3. Draw a line parallel to AB through P: Through point P, draw a line parallel to AB. This line will be the line on which points C and D lie.
4. Draw side BC: With B as center and radius 6.2 cm, draw an arc to intersect the parallel line through P at point C.
5. Complete parallelogram by drawing CD and AD: Join points C and D where D is the point on the parallel line through P such that AD = BC and AB || DC. Since ABCD is a parallelogram, AD is parallel and equal to BC.
   To find D, from A, draw an arc with radius equal to BC = 6.2 cm intersecting the parallel line through P at D.
6. Join all vertices: Join CD and AD to complete the parallelogram ABCD.

Parallelogram ABCD is constructed such that AB = 5 cm, BC = 6.2 cm and the altitude on AB is 3 cm, where AB and DC are base sides and BC and AD are the slanting sides parallel and equal. The altitude from points C and D to AB is equal to 3 cm, satisfying the height condition.