Use ruler and compasses to construct a parallelogram with diagonals 6 cm and 8 cm in length having given the acute angle between them is 60°. Measure one of the longer sides.

Steps of construction:

Let AC = 6 cm and BD = 8 cm.

1. Draw AO = $\dfrac{1}{2}AC = \dfrac{1}{2} \times 6 = 3\text{ cm and}$ produce AO to C such that OC = OA.
2. At O construct ∠COP = 60°.
3. From OP cut off OD = $\dfrac{1}{2} BD = \dfrac{1}{2} \times 8 = 4$ cm, produce DO to B such that OB = OD.
4. Join AB, BC, CD and DA. Then ABCD is the required parallelogram.

On measuring the length of longer side AD = BC = 6.1 cm.

Hence, length of longer side = 6.1 cm.