Question

The length of a rectangular hall is 5 m more than its breadth. The area of the hall is 750m^₂. FInd the perimeter of the hall.

Answer 1

Let breadth of the rectangular hall be b m.
Then, length of rectangular hall is (b + 5) m.
Area of rectangular hall = 750 m²
i.e., length × breadth = 750
$\Rightarrow$ (b + 5) × b = 750
$\Rightarrow$b² + 5b – 750 = 0
$\Rightarrow$ b² + 30b – 25b – 750 = 0
$\Rightarrow$ b (b + 30) – 25 (b + 30) = 0
$\Rightarrow$ (b + 30) (b – 25) = 0
$\Rightarrow$ b = –30 or 25
$\Rightarrow$ b = 25 (Breadth cannot be negative)

Now, length of hall = (b + 5) m
= (25 + 5) m
= 30 m
∴ Perimeter of hall = 2 (length + breadth)
= 2 (30 + 25) m
= 2 (55) m
= 110 m