The diagonal of a rectangular field is 16 m more than the shorter side. If the longer side is 14 m more than the shorter side, find the length and the breadth of the rectangular field.

Let the shorter side of the rectangular field be x m.

It is given that the diagonal of a rectangular field is 16 m more than the shorter side.

⇒ d = x + 16

And, the longer side is 14 m more than the shorter side.

⇒ l = x + 14

As we know that angles of rectangle are 90°. Using Pythagoras theorem,

⇒ diagonal² = length² + breadth²

⇒ (x + 16)² = (x + 14)² + x²

⇒ x² + 16² + 32x = x² + 14² + 28x + x²

⇒ x² + 256 + 32x = 2x² + 196 + 28x

⇒ 2x² + 196 + 28x - x² - 256 - 32x = 0

⇒ x² - 4x - 60 = 0

⇒ x² - 10x + 6x - 60 = 0

⇒ x(x - 10) + 6(x - 10) = 0

⇒ (x - 10)(x + 6) = 0

⇒ (x - 10) = 0 or (x + 6) = 0

⇒ x = 10 or x = -6

As length of shorter side cannot be negative,

Length = 10 + 14 = 24 m

Hence, length and breath of the rectangle = 24 m and 10 m.