IMO Square root (17).

For maximum length of diagonal I can find the G as (5,2) the distance between G and E the longest diagonal.
Thus ROOT[(5-1)^2 + (2-1)^2] = Sq Root (17) .

narik11 wrote:In a rectangular co ordinate system if the points E(1,1) F(2,2) H(4,1) G(X,Y) are the vertices of a parallelogram, what is the length of Longest diagonal of the parallelogram.

[spoiler]Answer 2 root(5)[/spoiler]

As with all geometry word problems, step 1 is to draw a diagram on your scrap paper.

Drawing this shape out, we quickly see that point G can be placed at (5,2) to create a parallelogram. (There are 3 other possible locations, but since the answers are all numbers (at least I'm assuming they are - please always include the choices!) we can choose any of the 4 possible points to complete our shape.)

Accordingly, the longest diagonal will run from (1,1) to (5,2). To solve for the diagonal, we use the right triangle running with the vertices (1,1), (5,1) and (5,2), giving us legs of 1 and 4. Applying the Pythagorean theorem:

1^2 + 4^2 = h^2
17 = h^2
root17 = h

The answer you provided doesn't match, so either you mistranscribed the question or the question is wrong. What's the source? (You should also always include the source of your questions!)

Answer is Sq Root (17)
Sorry made some mistake in calculation