Area and Perimeter

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Aptitude miscellaneous
  1. The perimeter of an isosceles triangle is 26 cm while equal sides together measure 20 cm. The third side and each of the equal sides are respectively.










  1. View Hint View Answer Discuss in Forum

    Let the third side be x.
    According to the question,
    x + 20 = 26

    Correct Option: A

    Let the third side be x.
    According to the question,
    x + 20 = 26
    ⇒ x = 26 - 20 = 6 cm
    ∴ Each equal side = 20/2 = 10 cm

  1. The ratio of length and breadth of a rectangle is 5 : 3 .If length is 8 m more than breadth, find the area of the rectangle.










  1. View Hint View Answer Discuss in Forum

    Let length of rectangle = 5k
    and breadth of rectangle = 3k

    According to the quecation,
    5k - 3k = 8

    Required area = Lenght x Breadth

    Correct Option: C

    Let length of rectangle = 5k
    and breadth of rectangle = 3k

    According to the quecation,
    5k - 3k = 8
    ⇒ 2k =8
    ∴ k = 4
    ∴ Lenght = 5k = 5 x 4 = 20 m
    Breadth = 3k = 3 x 4 = 12 m

    ∴ Required area = Lenght x Breadth
    = 20 x 12 = 240 sq m

  1. The ratio between the lenght and the breadth of a rectangle is 2 : 1. If breadth is 5 cm less than the length, what will be the parimeter of the rectangle?










  1. View Hint View Answer Discuss in Forum

    Let length = 2x and breadth = x
    According to the question,
    2x - x = 5

    ∴ Required perimeter = 2(2x + x)

    Correct Option: A

    Let length = 2x and breadth = x
    According to the question,
    2x - x = 5
    ⇒ x = 5

    ∴ Required perimeter = 2(2x + x)
    = 6x
    = 30 cm

  1. A person observed that he required 30 s time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30m/min, than the radius of the circular ground is (take π = 22/7)








  1. View Hint View Answer Discuss in Forum

    Let the radius of circular field = r m.
    Speed of person in m/s = 30/60 = 1/2m/s
    According to the question,
    [(2πr) /(1/2)] - [(2r)/(1/2)] = 30

    Correct Option: B

    Let the radius of circular field = r m.
    Speed of person in m/s = 30/60 = 1/2m/s
    According to the question,
    [(2πr) /(1/2)] - [(2r)/(1/2)] = 30
    ⇒ 4πr - 4r = 30
    ⇒ [4 x (22/7) - 4]r =30
    ⇒ (125 - 4)r = 30
    ⇒ (8.5)r = 30
    ⇒ r = 30/8.5 = 3.5 m

  1. A man riding a bicycle, completes one lap of a circular field along its circumference at the speed of 14.4 km/h in 1 min 28 s. What is the area of the field?










  1. View Hint View Answer Discuss in Forum

    The man takes 3600 s for 14.4 km
    The man will take 88 s for
    14.4 x (88/3600) = 352/1000 km = 352 m

    Now, circumference of circular field = 352 m
    ⇒ 2πr = 352 m
    2 x (22/7) x r = 352
    ⇒ r = 56 m

    Therefore, area of the field = πr2

    Correct Option: B

    The man takes 3600 s for 14.4 km
    The man will take 88 s for
    14.4 x (88/3600) = 352/1000 km = 352 m

    Now, circumference of circular field = 352 m
    ⇒ 2πr = 352 m
    2 x (22/7) x r = 352
    ⇒ r = 56 m

    Therefore, area of the field = πr2
    = (22/7) x 56 x 56
    = 8 x 22 x 56 m2
    = 9856 sq m.