Question
Construct a parallelogram, one of whose sides is $4.4\ cm$ and whose diagonals are $5.6\ cm$ and $7\ cm.$ Measure the other side.
✓
Answer
We know that the diagonals of a parallelogram bisect each other.
Steps of construction:
Step 1: Draw $AB = 4.4\ cm.$
Step 2: With $A$ as the centre and radius $2.8\ cm$, draw an arc.
Step 3: With $B$ as the centre and radius $3.5\ cm,$ draw another arc, cutting the previous arc at point $O.$
Step 4: Join $OA$ and $OB.$
Step 5: Produce $OA$ to $C,$ such that $OC = AO.$ Produce $OB $ to $D,$ such that $OB = OD.$
Step 6: Join $AD, BC,$ and $CD.$ Thus, $ABCD$ is the required parallelogram.
The other side is $4.5\ cm$ in length.
Steps of construction:
Step 1: Draw $AB = 4.4\ cm.$
Step 2: With $A$ as the centre and radius $2.8\ cm$, draw an arc.
Step 3: With $B$ as the centre and radius $3.5\ cm,$ draw another arc, cutting the previous arc at point $O.$
Step 4: Join $OA$ and $OB.$
Step 5: Produce $OA$ to $C,$ such that $OC = AO.$ Produce $OB $ to $D,$ such that $OB = OD.$
Step 6: Join $AD, BC,$ and $CD.$ Thus, $ABCD$ is the required parallelogram.
The other side is $4.5\ cm$ in length.
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