Question
Construct a rhombus the lengths of whose diagonals are $6\ cm$ and $8\ cm.$
✓
Answer
We know that the diagonals of a rhombus bisect each other.
Steps of construction:
Step 1: Draw $AC = 6\ cm.$
Step 2: Draw a perpendicular bisector $(XY)$ of $AC,$ which bisects $AC$ at $O.$
Step 3: $\text{OB}=\frac{1}{2}(8)\text{cm}$ $\text{OB}=4\text{cm}$ and $\text{OD}=\frac{1}{2}(8)\text{cm}$ Draw an arc of length $4\ cm$ on $OX$ and name that point as $B.$ Draw an arc of length $4\ cm$ on $OY$ and name that point as $D.$
Step 4: Join $AB, BC, CD$ and $AD.$ Thus, $ABCD$ is the required rhombus, as shown in the figure.
Steps of construction:
Step 1: Draw $AC = 6\ cm.$
Step 2: Draw a perpendicular bisector $(XY)$ of $AC,$ which bisects $AC$ at $O.$
Step 3: $\text{OB}=\frac{1}{2}(8)\text{cm}$ $\text{OB}=4\text{cm}$ and $\text{OD}=\frac{1}{2}(8)\text{cm}$ Draw an arc of length $4\ cm$ on $OX$ and name that point as $B.$ Draw an arc of length $4\ cm$ on $OY$ and name that point as $D.$
Step 4: Join $AB, BC, CD$ and $AD.$ Thus, $ABCD$ is the required rhombus, as shown in the figure.
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