Question

Construct a parallelogram ABCD in which AB = 5 cm, BC = 4.8 cm and height corresponding to AB is 3.5 cm.

Answer 1

Given: AB = 5 cm, BC = 4.8 cm, height (altitude) corresponding to AB = 3.5 cm.

Step-wise calculation (Construction):

1. Draw the segment AB = 5 cm.
2. At A, construct a line perpendicular to AB. At B construct a line through B perpendicular to AB.
3. On the perpendicular at A mark point M so that AM = 3.5 cm measured away from AB. On the perpendicular at B mark point N so that BN = 3.5 cm.
4. Join M and N. The line MN is parallel to AB and is at the required distance 3.5 cm from AB.
5. On MN, from N measure and mark point C so that NC = BC = 4.8 cm. Choose a direction along MN for C. From M measure and mark point D in the same direction so that MD = 4.8 cm.
6. Join B to C and A to D. Also join C to D. ABCD is then a parallelogram with AB = 5 cm, BC = 4.8 cm and the altitude to AB equal to 3.5 cm.

Parallelogram ABCD constructed as above satisfies AB = 5 cm, BC = 4.8 cm and the height corresponding to AB = 3.5 cm.