Question

To draw a parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm and to state whether it is unique.

Answer 1

Hint: For solving this problem, we need to know the basics of construction and the basic properties to parallelogram and draw its figure and to find whether it is unique or whether many other parallelograms can exist with this condition.

Complete step by step answer:

We first understand the basics of parallelogram before solving the problem. A parallelogram is a quadrilateral with two parallel sides with the parallel sides being equal to each other. A parallelogram looks like one shown below.

To construct the parallelogram, we first start by drawing a line KA = 4.2 cm. Then, we start by constructing an angle from the point K. Let the angle made with side KA be x degrees. Then, we construct a supplementary angle [ (180-x) degrees] from the point A such that the angle it makes with side KA is (180-x) degrees.

Now, we draw a line from point K with the constructed angle x and then using a compass, we cut an arc by taking a length of 5.5 cm. Name the point where the arc intersects the line as OF. Now, we draw a line from point A with the constructed angle (180-x) and then using a compass, we cut an arc by taking a length of 5.5 cm. Name the point where the arc intersects the line as Y. We join AY, KO and OY. We have now constructed the parallelogram OKAY (will look as shown in the figure).

Clearly, this parallelogram is not unique since the angle constructed x can have any value. Thus, we could have multiple parallelograms with different values of x.

Note: It is important to note that while constructing the angle x, one can have any value between 0 and 180 degrees (exclusive of 0 and 180 degrees). Further, for x = 90 degrees, we would have the special case of a rectangle. Further, in the problem, the angle can be constructed using a protractor.