Step 1: Draw AB = 5cm.

Step 2: At B, draw an angle of ${45}^{\circ }$ and mark 6 cm along that angle. Mark the point as C.

Step 3: At C, draw an angle of ${55}^{\circ }$ and mark 7cm along that angle. Mark the point as D.

Step 4: Join point A and D. So, quadrilateral ABCD can be constructed.

We know that we need minimum 5 measurements from a quadrilateral to draw it.
In one option we have 5 measurements as AB, BC, CD, DA and BD. Here AB, BC, CD, DA are sides and BD is a diagonal.
The construction is possible.
AB, BC, CD, AC and BD. These are 3 sides and 2 diagonals. So, it is possible to construct the quadrilateral.
In other two options only 4 sides and 2 sides are mentioned. So construction is not possible.

Since all the sides of a rhombus are equal, it means that if we know one side we know all the sides.

Now,  while constructing the rhombus we need to know at least one angle (as all the angles in a rhombus are not equal). Therefore, in total we need at least 2 measurements to construct a unique rhombus.

Any four measurements are not sufficient to draw a unique quadrilateral.
Let us take AB = 5cm, BC = 4cm, AD = 5cm, CD = 3cm.

We shall start constructing with any one side (say AB). Construct AB with length 5cm. Now, as we have BC and AD. We can draw arcs with BC and AD as radii. But we cannot mark the points C and D based on the data given. So, we need more data to draw a quadrilateral.

Rectangle is a special quadrilateral and minimum number of measures required to construct a rectangle is 2(length of 2 sides).
Since we only know one side of the rectangle. we can draw infinite rectangles. This is because the other side's length is not specified. For e.g.

Let us try to draw the quadrilateral:

Step 1: Draw BC = 6 cm.

Step 2: At B, draw an angle = ${60}^{\circ }$. Along that angle, make an arc of 5 cm and mark it as point A.

Step 3: From A, draw an arc of 6 cm.

Step 4: From C, draw an arc of 7 cm such that it intersects the arc made from A. Mark the point of intersection as D.

Step 5: Join ABCD to complete the quadrilateral.

Is this quadrilateral unique? Yes it is.

If we move it, keeping all the angle length constant $△$ ABC will change. So, there is only one quadrilateral ABCD with AB = 5 cm, BC = 6 cm, CD = 7 cm, BA = 6 cm, $\angle$ ABC= ${60}^{\circ }$.

Since one side of a triangle cannot be greater than the sum of the other two sides, diagonal LY must be smaller than the sum of PL + PY and smaller than the sum of AL + AY. PL + PY =5 and AL + AY = 8.5. Hence, LY must be less than 5. Thus, the correct answer is 6.

To construct a parallelogram both unequal sides need to be provided. Other than this one angle or one diagonal should be provided. Hence, a minimum of 3 measurements are needed.

Drawing a line segment, which lies in between two given angles, is the first step in this construction. After the line segment is constructed, angles are drawn using that line segment as the base.

Minimum number of measures required to construct a rhombus are 2.
If one side of a rhombus is specified, another measurement that must be specified to construct a rhombus is its diagonal or one of the angles.
Thus, the correct answer is AC as it is diagonal.