LET the shorter side of the rectangular field be 'x' meters.

Therefore the LONGER side will be (x + 30) meters.

And the LENGTH of the diagonal will be (x + 60) meters.

Now, according to the question,

The diagonal divides the rectangular into two right angledtriangles and the diagonal is the common side of the two triangles and it isalso the LONGEST side of the triangles i.e. the hypotenuse.

So, by Pythagoras Theorem,

(Diagonal)² = (Smaller Side)² + (Longer Side)²

(x + 60)² = (x)² + (x + 30)²

x² + 120x + 3600 = x² + x² + 60x + 900

x² + 60x - 120x + 900 - 3600 = 0

x² - 60x - 2700 = 0

x² - 90x + 30x - 2700 = 0

x(x - 90) + 30(x - 90) = 0

(x - 90) (x + 30) = 0

x = 90 because x = - 30 as length cannot be possible.

So the length of the shorter side is 90 meters and thelength of the longer side is 90 + 30 = 120 meters.

There’s an alternate method too:

Let the shorter side of the rectangle be x m.
Then, larger side of the rectangle = (x + 30) m

⇒ x2 + (x + 30)2 = (x + 60)2
⇒ x2 + x2 + 900 + 60x = x2 + 3600 + 120x
⇒ x2 - 60x - 2700 = 0
⇒ x2 - 90x + 30x - 2700 = 0
⇒ x(x - 90) + 30(x -90)
⇒ (x - 90)(x + 30) = 0
⇒ x = 90, -30
However, side cannot be negative. Therefore, the length ofthe shorter side will be 90 m.
Hence, length of the larger side will be (90 + 30) m = 120 m.

Hope This Helps :)