The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side,

Solution:

Let the length of the shorter side be x metres.

Thus the length of the longer side=(x+30) m

Length of the diagonal=(x+60)m

Each angle of a rectangle=90 degrees

By Pythagoras Theorem, (diagonal)²=(shorter side)²+(longer side)²

(x+60)²  = x²+(x+30)²

x²-60x-2700=0  => (x+30)(x-90)=0  => x=-30 or x=90

As the length of a side cannot be negative,the length of the shorter side = 90 m.

Thus the length of the longer side=120 m

Let the shorter side be ‘a’. 

Given, diagonal of a rectangular field is 60 metres more than the shorter side 

Diagonal = a + 60 

Also, longer side is 30 metres more than the shorter side 

Longer side = a + 30 

Hypotenuse² = length² + breadth² 

⇒ (a + 60)² = (a + 30)² + a² 

⇒ a² + 120a + 3600 = a² + 60a + 900 + a² 

⇒ a² – 60a – 2700 = 0 

⇒ a² – 90a + 30a – 2700 = 0 

⇒ a(a – 90) + 30(a – 90) = 0 

⇒ (a + 30)(a – 90) = 0 

⇒ a = 90m 

Length of sides = 90m, 120 m