Question 924438
Perimeter = 2 x Length + 2 x width
Length = x
Width = y
Perimeter = 2x + 2y
2x + 2y = 60 
2y = 60 - 2x
2y = 2(30 - x)
Divide both sides by 2
y = 30 - x

Using the diagonal.
x^2 + y^2 = 25^2 (Pythagoras theorem)
Substitute y = 30 - x
x^2 + (30 - x)^2 = 625
Multiply out bracket
x^2 + 900 - 60 x + x^2 = 625
Collect like terms
2x^2 - 60x + 900 - 625 = 0
2x^2 - 60x + 275 = 0
Your answer.

Hope this helps.
:-)