Construct a parallelogram, one of whose sides is 4.4 cm and whose diagonals are 5.6 cm and 7 cm.

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.

Solution:

We know that the diagonals of a parallelogram bisect each other.

Steps of construction:

Step 1: Draw $A B=4.4 \mathrm{~cm}$

Step 2: With $A$ as the centre and radius $2.8 \mathrm{~cm}$, draw an arc.

Step 3: With $B$ as the centre and radius $3.5 \mathrm{~cm}$, draw another arc, cutting the previous arc at point $O$.

Step 4: Join $O A$ and $O B$.

Step 5: Produce $O A$ to $C$, such that $O C=A O$. Produce $O B$ to $D$, such that $O B=O D$.

Step 5: Join $A D, B C$, and $C D$.

Thus, ABCD is the required parallelogram. The other side is 4.5 cm in length.

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