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, find the sides of the field
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