Question

A society decides to build a prayer hall having a carpet area of 300 sq. meter with its
length 1 m more than twice its breadth. Find the length and breadth of the hall.

Answer 1

Answer:

$\red\bigstar$ Length of the prayer hall = 25m.

$\blue\bigstar$ Breadth of the prayer hall = 12m.

$\dag$SOLUTION$\dag$

Area of the prayer hall = 300m². (Carpet area = Area of the hall)

Let us assume that the breadth of the prayer hall = 'b'

∵ It is said that length is 1 m more than twice its breadth.

⇒ Length of the prayer hall = (2b + 1) $\longrightarrow$(1)

Area of a rectangle = l × b , Where l is the length and b is the breadth of the rectangle.

Here,

Area = 300m²

l = (2b +1)

b = b

⇒ Area of the prayer hall = (2b +1) × b

⇒ 300 = 2b² + b

⇒ 2b² + b - 300 = 0

Now, let us factorize , 2b² + b - 300 = 0 by middle term splitting.

Product = -600

Sum = 1

⇒ 2b² + 25b - 24b - 300 = 0

⇒ b(2b + 25) - 12(2b + 25)

⇒ (b - 12)(2b + 25)

⇒ b = 12 or b = -25/2.

∵ b is the breadth of a rectangle it cannot take a negative value .

∴ b = 12m.

Now, from (1)

Length of the prayer hall = (2b + 1)

⇒ Length of the prayer hall = 2 × 12 + 1

⇒ Length of the prayer hall = 25m.

THE HALL

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