The diagonal of a rectangular field is 60 m more than the shorter side. If the longer side is 30 m more than the shorter side, then the sides are :

1. 60 m, 90 m

2. 80 m, 110 m

3. 90 m, 120 m

4. 110 m, 140 m

Let the shorter side of rectangular field be x meters.

Given,

The diagonal of rectangular field is 60 m more than shorter side.

Diagonal = (x + 60) meters

Given,

The longer side of rectangle is 30 m more than shorter side, Let the longer side be z,

Longer side = (x + 30) meters

By pythagoras theorem,

In a rectangular field,

⇒ Hypotenuse² = Shorter side² + Longer side²

⇒ (x + 60)² = x² + (x + 30)²

⇒ [x² + (60)² + 2 × x × 60] = x² + [x² + (30)² + 2 × x × 30]

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

⇒ x² + 3600 + 120x = 2x² + 900 + 60x

⇒ 2x² + 900 + 60x - x² - 3600 - 120x = 0

⇒ 2x² - x² + 60x - 120x - 3600 + 900 = 0

⇒ x² - 60x - 2700 = 0

⇒ x² - 90x + 30x - 2700 = 0

⇒ x(x - 90) + 30(x - 90) = 0

⇒ (x + 30)(x - 90) = 0

⇒ (x + 30) = 0 or (x - 90) = 0     [Using zero -product rule]

⇒ x = -30 or x = 90

Since length of rectangle cannot be negative x ≠ -30

The longer side of rectangle is,

x + 30 = 90 + 30 = 120 meters.

Thus, sides are 90 m and 120 m.

Hence, option 3 is the correct option.