If the diagonal and the area of a rectangle are 25 m² and 168 m², what is the length of the rectangle?

Let the length of the rectangle be x metre.
Then, a breath of the rectangle = (168/x)

∴ √{(x)² + (168/x)²} = 25
⇒ √{(x² + (28224/x²)} = 25
⇒ {(x² + (28224/x²)} = 625
⇒ x⁴ - 625x² + 28224 = 0
⇒ x²(x² - 576) - 49(x² - 576) = 0
⇒ (x² - 576)(x² - 49) = 0
⇒ x² = 576 or x² = 49
⇒ x = 24 or x = 7

Hence, length = 24 cm. and breadth = 7 m.