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Aptitude miscellaneous
  1. The perimeter and length of a rectangle are 40 m and 12 m respectively. Its breadth will be








  1. View Hint View Answer Discuss in Forum

    Using Rule 9,
    Perimeter of rectangle = 40 metre
    Length = 12 metre
    ∴ 2(l + b) = 40
    ⇒ 2 (12 + b) = 40

    ⇒ 12 + b =
    40
    		 = 20
    2

    ⇒ b = 20 – 12 = 8 metre

    Correct Option: B

    Using Rule 9,
    Perimeter of rectangle = 40 metre
    Length = 12 metre
    ∴ 2(l + b) = 40
    ⇒ 2 (12 + b) = 40

    ⇒ 12 + b =
    40
    		 = 20
    2

    ⇒ b = 20 – 12 = 8 metre

  1. If the perimeter of a square and a rectangle are the same, then the area P and Q enclosed by them would satisfy the condition








  1. View Hint View Answer Discuss in Forum

    Using Rule 10,
    Let the side of square be 1 cm, then 2 (l + b)
    = 4 × side = 4 × 1
    ⇒ l + b = 2, If l = 1.5, b = 0.5
    ∴ Area of square = 1 sq.cm.
    and Area of rectangle = 1.5 × 0.5 = 0.75 sq.cm.
    For a given perimeter, square has the largest area. i.e, P > Q

    Correct Option: C

    Using Rule 10,
    Let the side of square be 1 cm, then 2 (l + b)
    = 4 × side = 4 × 1
    ⇒ l + b = 2, If l = 1.5, b = 0.5
    ∴ Area of square = 1 sq.cm.
    and Area of rectangle = 1.5 × 0.5 = 0.75 sq.cm.
    For a given perimeter, square has the largest area. i.e, P > Q

  1. PQRS is a square with side 10 cm. A, B, C and D are mid–points of PQ, QR, RS and SP respectively. Then the perimeter of the square ABCD so formed is








  1. View Hint View Answer Discuss in Forum


    PA = AQ = QB = 5 cm.
    ∴ ∠AQB = 90°
    ∴ AB = √AQ² + QB²
    = √5² + 5² = √25 + 25
    = √50 = 5√2 cm.
    ∴ Perimeter of ABCD = 4 × 5√2 = 20√2 cm.

    Correct Option: B


    PA = AQ = QB = 5 cm.
    ∴ ∠AQB = 90°
    ∴ AB = √AQ² + QB²
    = √5² + 5² = √25 + 25
    = √50 = 5√2 cm.
    ∴ Perimeter of ABCD = 4 × 5√2 = 20√2 cm.

  1. A piece of wire when bent to form a circle will have a radius of 84 cm. If the wire is bent to form a square, the length of a side of the square is








  1. View Hint View Answer Discuss in Forum

    Using Rule 14,
    Length of wire = Circumference of circle = 2πr

    = 2 ×
    22
    		 × 84 = 528 cm.
    2

    ∴ Perimeter of square = 528 cm.
    ⇒ 4 × side = 528
    ⇒ Side =
    528
    		 = 132 cm.
    4

    Correct Option: B

    Using Rule 14,
    Length of wire = Circumference of circle = 2πr

    = 2 ×
    22
    		 × 84 = 528 cm.
    2

    ∴ Perimeter of square = 528 cm.
    ⇒ 4 × side = 528
    ⇒ Side =
    528
    		 = 132 cm.
    4

  1. The perimeters of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 9 cm. Determine the corresponding side of the second triangle.








  1. View Hint View Answer Discuss in Forum

    If the required side be x cm, then

    30
    		 =
    9
    20x

    ⇒ 3x = 9 × 2
    ⇒ x =
    9 × 2
    		 = 6 cm.
    3

    Correct Option: B

    If the required side be x cm, then

    30
    		 =
    9
    20x

    ⇒ 3x = 9 × 2
    ⇒ x =
    9 × 2
    		 = 6 cm.
    3