Question

Construct a Rhombus PQRS such that PR = 8cm, QS = 5.4cm.

Answer 1

Hint: Rhombus is a type of quadrilateral with special properties such as the diagonals of Rhombus are perpendicular bisectors of each other. And all the sides of Rhombus must be equal to each other and must be congruent to each other. These properties will help us in construction of the Rhombus PORS.

Complete step-by-step answer:
First of all we know that by the property of Rhombus that all the sides of Rhombus must be equal to each other and PR = 8cm QS = 5.4cm ( both are diagonals ).
Now let us solve the question step by step so that you will understand it easily.
Step 1. Let us draw a line segment PR = 8cm.
Step 2. Now bisect PR and mark its midpoint as O.
Step 3. Now put the compass on point P and draw an arc and similarly put the compass on point R and draw an arc again to cut the perpendicular bisector of the line segment PR at Q and S.
Step 4. Now as the total length of QS = 5.4cm so the radii of this perpendicular bisector must be 2.7cm with the centre O.
Step 5. Now join the points PQ , QR, RS and PS.
So, after following these steps we will come up with a figure as shown below.

And hence Rhombus PQRS will be formed.

Note:Whenever we come up with a question of construction we must have our construction materials and we must know that the perpendicular bisector of any line segment must be drawn at exactly the middle point of that line segment. Properties of rhombus are very important for construction of any Rhombus.