Question

The diagonal of a rectangular field is 15 metres and the difference between its length and width is 3 metres. The area of the rectangular field is :

(a) 9 m² 

(b) 12 m² 

(c) 21 m² 

(d) 108 m² 

Answer 1

(d) 108 m²

Let the length of the field be x m 

Then, width of the field = (x + 3)m

Then x² + (x + 3)² = 15²             (pyth. Th.)

⇒ x² + x² + 6x + 9 = 225

⇒ 2x² + 6x - 216 = 0

⇒ x² +3x - 108 = 0

⇒ (x + 12 )(x - 9) = 0 ⇒ x = -12,9

∴ Rejecting the negative value, length = 9 m

∴ Width = 12 m 

⇒ Area of the field = 12 m × 9 m = 108 m².