The length of a rectangular hall is 5 m more than its breadth. If the area of the hall is 594 m², find its perimeter.

Let breadth = x meters

So, length = (x + 5) meters

We know that,

Area of rectangular hall = length × breadth

Substituting the values we get,

⇒ 594 = x(x + 5)

⇒ 594 = x² + 5x

⇒ x² + 5x – 594 = 0

⇒ x² + 27x – 22x – 594 = 0

⇒ x(x + 27) – 22(x + 27) = 0

⇒ (x – 22)(x + 27) = 0

⇒ x – 22 = 0 or x + 27 = 0

⇒ x = 22 or x = -27.

Since, length of side cannot be negative so, x ≠ -27.

∴ Breadth = x = 22 m and Length = (x + 5) = 22 + 5 = 27 m.

Perimeter = 2(l + b)

Substituting the values we get,

Perimeter = 2(27 + 22) = 2 × 49 = 98 m.

Hence, perimeter of hall = 98 m.