A path of uniform width of 2.5 m runs outside a square field all around. What will be the length of the side of the square field, if the area of the path is 625 sq. m?

The correct answer is (c) 50 m.

Let $x$ be the length of the side of the square field. The area of the square field is $x^2$. The area of the path is $x^2 – (x+2.5)^2 = 625$. Expanding the right-hand side, we get $x^2 – 2x – 6.25 = 0$. Factoring, we get $(x-25)(x+2.5) = 0$. Therefore, $x = 25$ or $x = -2.5$. Since the length of a side of a square cannot be negative, the length of the side of the square field is $x = 25$ m.

The other options are incorrect because they are not the lengths of the sides of a square with an area of 625 square meters.