We will assume the park is rectangular and that we need to find the sides.

Let

S = the shorter side, S>=0

L = the longer side, L>=0

D = the diagonal of the park, D>=0

The diagonals of the rectangular park plus its longer sides together measure 7 times one of the shorter sides:

2D + 2L = 7S

The length of one diagonal is 250 m longer than one of the shorter sides means:

D = 250 + S

Finally, using the Pythagorean Theorem:

D^2 = L^2 + S^2

We have three equations with three unknown variables.

Plug D = 250 + S into 2D + 2L = 7S and solve for L:

2(250 + S) + 2L = 7S

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click here to see the equation solved for L

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L = (5/2)(S - 100)

Now plug D = 250 + S and L = (5/2)(S - 100) into D^2 = L^2 + S^2:

(250 + S)^2 = ((5/2)(S - 100))^2 + S^2

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click here to see the equation solved for S

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S = 280 m

L = (5/2)(280 - 100)

L = 450 m

The dimensions of the park are: the longer side is 450 m and the shorter side is 280 m.