Question & Answer

Construct a parallelogram ABCD, in which AB=6cm, BC=4.2cm and the height from AB=3.5cm.

ANSWER Verified Verified
Hint: We should draw the base AB upon which the given height is to be drawn. Then we may draw two perpendicular lines on the base at any two points and cut at 3.5cm on both the perpendiculars from their intersection points from the base and join them. Then we can take an arc of length 4.2cm from B and cut it on the line drawn through the perpendiculars and join B and this point of intersection to get the side BC. Now we can cut the line through the perpendiculars at 6cm from C and name it D. Finally, we can join A and D.

Complete step-by-step answer:

The above figure shows the parallelogram. The steps to construct it are:
Step 1- We can choose a point B and draw a line through it. Cut it at a distance of 6cm from B by an arc and name it A.
Step 2- We now draw two perpendiculars through any two points on AB. Name the points of intersections as R and S.
Step 3- We can cut the two perpendiculars by arcs at 3.5cm from R and S and name them P and Q respectively. Draw a line P and Q.
Step 4- We then cut PQ at 4.2cm by an arc from B and name the point of intersection as C. Join B and C.
Step 5- Finally, we cut PQ by an arc at 6cm from C at the side of A and name it D. At last, we join A and D to obtain the required parallelogram.
$\therefore $ ABCD is the required parallelogram with AB=CD=6cm, BC=AD=4.2cm and a height of 3.5cm.

Note: We should not build D at the opposite side of A in step 5 as D should lie on the same side of C as A lies of B, otherwise a parallelogram would not be formed.