Theory:

Let's see how to construct a quadrilateral when two diagonals and three sides are given.
Example:
Draw a quadrilateral \(PLAN\), where \(LA = 5 \ cm\), \(PN = 4.5 \ cm\), \(AN = 4 \ cm\), diagonal \(PA = 5.5 \ cm\) and the diagonal \(LN = 7 \ cm\).
 
Rough diagram:
 
Let us first draw the rough quadrilateral, which will help us to draw a fair quadrilateral.
 
Rou_2 (1).png
 
Fair diagram:
 
Step 1: Draw a line segment \(PA = 5.5 \ cm\).
 
LI_6.png
 
Step 2: Given that \(PN = 4.5 \ cm\) and \(AN = 4 \ cm\). Take \(4.5 \ cm\) as radius and draw an arc from point \(P\). Then, take \(4 \ cm\) as another radius and draw an arc from point \(A\), which cuts the previously drawn arc.
 
LI_7.png
 
Step 3: Mark the two arcs meeting point as \(N\), then join \(PN\) and \(AN\).
 
LI_8.png
 
Step 4: Also, given that \(LA = 5 \ cm\) and \(LN = 7 \ cm\). Take \(5 \ cm\) as radius and draw an arc from point \(A\). Then, take \(7 \ cm\) as another radius and draw an arc from \(N\), which cuts the previously drawn arc.
 
LI_9.png
 
Step 5: Mark the two arcs meeting point as \(L\), then join \(NL\), \(AL\) and \(PL\). We obtained the required quadrilateral \(PLAN\).
 
LI_10.png