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Mathematics

Statement I: A room has two doors of equal dimensions. The perimeter of each door is 7 m. The sum of their widths is 3 m. Therefore, the height of each door is 2 m.

Statement II: Length of the rectangle = 12\dfrac{1}{2} perimeter + width

  1. Statement I is true but statement II is false.

  2. Statement I is false but Statement II is true.

  3. Both Statement I and Statement II are true.

  4. Both Statement I and Statement II are false.

Mensuration

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Answer

Statement I:

Sum of widths of two equal doors = 3 m

So, width of each door = 32\dfrac{3}{2} = 1.5 m

Perimeter of each door = 7 m

Perimeter = 2(length + width)

⇒ 7 = 2(height + 1.5)

⇒ 72\dfrac{7}{2} = height + 1.5

⇒ 3.5 = height + 1.5

⇒ height = 3.5 - 1.5

⇒ height = 2 m. Statement I is true.

Statement II:

Perimeter of rectangle = 2(length + width)

⇒ 12\dfrac{1}{2} × Perimeter = length + width

⇒ Length = 12\dfrac{1}{2} Perimeter - width

So, the correct formula is Length = 12\dfrac{1}{2} perimeter - width, not + width. Statement II is false.

Statement I is true but Statement II is false.

Hence, option 1 is the correct option.

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