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Quiz: Perimeter and Area

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Number of Questions: 31

Question: 6 -

The length of a rectangle is increased by 60%. By what percent would the width have to be decreased to maintain the same area?

Options:

  1. 120%

  2. 60%

  3. 75%

  4. 37.5%

    5. Answer:

    37.5%
    Solution:

    Let the length of the rectangle be x and breadth be y

    Then, Area = L x B = xy
    New length =Area Aptitude

    Area Aptitude

Question: 7 -

If the diagonal of a square field is 16 m, what is its area?

Options:

  1. 126 m2

  2. 130 m2

  3. 128 m2

  4. 132 m2

    5. Answer:

    128 m2
    Solution:

    Area of a square:
    (Side)2 = Area Aptitude× (diagonal)2

                             = Area Aptitudex (16)2

                             = Area Aptitudex 256

                             = 128 m2

Question: 8 -

The area of a rectangle and square are equal. The side of the square is 5 cm and the smaller side of the rectangle is half that of the square. The length of the other side of the rectangle would be

Options:

  1. 8 cm

  2. 12.5 cm

  3. 10 cm

  4. 5 cm

    5. Answer:

    10 cm
    Solution:

    Side of Square = 5 cm, and length of one side of rectangle = 5/2 = 2.5 cm

    Let the length of the other side of the rectangle = B

    As per the question:

    Area of rectangle = Area of square

    Length x Breadth = Side x Side
                    2.5 * B = 5 * 5
                             B = 25/2.5
                             B = 10 cm

Question: 9 -

The ratio between the breadth and perimeter of a rectangle is 2:10. If the area of the rectangle is 428 sq. cm, what is the length of the rectangle?

Options:

  1. 30.4 cm

  2. 45.4 cm

  3. 40.4 cm

  4. 25.4 cm

    5. Answer:

    25.4 cm
    Solution:

    Perimeter of a rectangle = 2 (Length + Breadth)

    Let length is L and breadth is B.

    So, as per the question = 2(L+B)/B = 10/2
                                         2(L+B)/B = 5/1
                                         2L + 2B = 5B
                                         2B - 5B = - 2L
                                         - 3B = - 2L
                                         B = 2/3 L

    Given Area = 430 sq. cm.

    Area = Length * Breadth
             430 = L * 2/3 L
             430 = 2/3 L2

    Or L2 = 1290 / 2
       L2 = 645
       L = 25.4 cm

Question: 10 -

If the perimeter of a square is 24 cm, one of the sides of the square is

Options:

  1. 8 cm

  2. 2 cm

  3. 12 cm

  4. 6 cm

    5. Answer:

    6 cm
    Solution:

    Perimeter of Square = 4 x side
                                      4 x side = 24
                                      Side = 24/4 = 6 cm
                                      One of the sides of the square is 6 cm.