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.

Fair diagram:

Step 1: Draw a line segment $$PA = 5.5 \ cm$$.

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.

Step 3: Mark the two arcs meeting point as $$N$$, then join $$PN$$ and $$AN$$.

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.

Step 5: Mark the two arcs meeting point as $$L$$, then join $$NL$$, $$AL$$ and $$PL$$. We obtained the required quadrilateral $$PLAN$$.