Question

The area of a rectangular prayer hall is 300 m2. If the length of the hall
(in metres) is one more than twice its its breadth, then find the dimensions
of the prayer hall.​

Answer 1

Given that, The area of a rectangular prayer hall is 300 m². The length of the hall is one more than twice its Breadth.

Need to find: The dimensions of the prayer hall.

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Let the Breadth of the Rectangular prayer hall be x m.

$\therefore$ Length of the rectangular prayer hall be (2x + 1) m.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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$\star\;\boxed{\sf{\pink{Area_{\;(rectangle)} = Length \times Breadth}}}$

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• Area of the rectangular prayer hall is given that is 300 m². Comparing with Formula,

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Therefore,

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$:\implies\sf 300 = (2x + 1) \times x \\\\\\:\implies\sf 300 = 2x^2 + x \\\\\\:\implies\sf 2x^2 + x - 300 = 0 \\\\\\:\implies\sf 2x^2 + 25x - 24x - 300 = 0 \\\\\\:\implies\sf x(2x + 25) -12(2x + 25) = 0 \\\\\\:\implies\sf (x - 12) \;or\; (2x + 25) = 0 \\\\\\:\implies{\underline{\boxed{\frak{\pink{ x = 12 \; or \; x = \dfrac{-25}{2}}}}}}\;\bigstar$

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• By ignoring the negative value, because any side can't be negative. Taking, x = 12.

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Hence,

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• Length of the Hall, x = {2(12) + 1} = (24 + 1) = 25 m
• Breadth of the Hall, x = 12 m.

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$\therefore{\underline{\sf{Hence,\; Length\;and\; Breadth\;of\;Hall\:are\; \bf{25\;m\;\&\;12\;m }.}}}$

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Answer 2

Given

• Area of rectangular prayer hall = 300 m²
• Length of hall = one more twice its breadth

To find

• Length of hall
• Breadth of hall

Solution

Let the breadth of hall be x cm, then according to the question, length is one more twice its breadth, so length of hall is 2x + 1

Then, solving the problem with the formula of area of rectangle :-

• Area = Length × Breadth
• 300 = (2x + 1) × (x)
• 300 = 2x² + x
• 2x² + x - 300 = 0  
• 2x² + 25x - 24x - 300 = 0
• x (2x + 25) - 12(2x + 25) = 0
• (x - 12) = 0 or  (2x + 25) = 0
• x = 12 or x = -25/2

Since, the value of side of rectangle or any other figure like square, circle cannot be negative, we consider the positive value.

Hence, the value of x is 12

The dimensions are

Length :-

• (2x + 1)
• (2(12) + 1)
• 24 + 1
• 25

Hence, the length of the rectangular prayer hall is 25 m

Breadth :-

• (x)
• 12

Hence, the breadth of the rectangular prayer hall is 12 m

Verification

• Area = Length × Breadth
• 300 = 25 × 12
• 300 = 300
• L.H.S = R.H.S

Learn more

• Area of square = side × side
• Area of rectangle = 1/2 × base × height
• Area of parallelogram = base × height
• Area of trapezium = 1/2 h (sum of parallel sides)