SOLUTION: A field in the from of a parallelogram has an area of 432 m2 find the length of its diagonal on which the perpendiculars drawn from two vertices on either side of it are 12m long.

Make a sketch. Draw the diagonal and two perpendiculars from the vertices of the parallelogram to this diagonal. 

The diagonal divides the parallelogram in two congruent triangles.
Do you know it? If not, look into the lesson In a parallelogram, each diagonal divides it in two congruent triangles in this site. 

Notice, that perpendiculars drown to the diagonal are altitudes in the triangles.

Now, the area of each of these two triangles is half of the product of the diagonal measure and the altitude, 
i.e. , where x is the unknown length of the diagonal.

The sum of these areas is the area of the parallelogram, which is given.

So, you have this equation to find the length of the diagonal:

12*x = 432.

Hence, x =  = 36 m.

Answer. The length of the diagonal is 36 m.