Question

The diagonal of a rectangular field is 25 metres more than the shorter side. If longer side is 23 metres more than the shorter side, find the sides of the field.

Answer 1

Let the shorter side be x m.

Then diagonal = (x + 25)m and longer side = (x + 23 )m.

We known that each angle of a rectangle is 90°.

In a right ∆ABC, we have (x + 25)² = (x + 23)² + x²

x² + 50x + 625 = x² + 46x + 529 + x²

⇒ 2x² + 46x + 529 – x² – 50x – 625 = 0

⇒ x² – 4x — 96 = 0

⇒ x² – (12 – 8)x – 96= 0

⇒ x² – 12x + 8x – 96 = 6

⇒ (x² – 12x) + (8x – 96) = 0

⇒ x(x – 12) + 8(x – 12) = 0

⇒ (x – 12) (x + 8) = 0

⇒ x – 12 = 0 and x + 8 = 0

⇒ x = 12 and x= – 8 (Reject)

Hence, longer side = 12 + 23 i.e., 35 m and shorter side = 12 m.