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Home ‣ Aptitude ‣ Volume and Surface Area Comments
  • Question

  • Consider the following statements: 1) The perimeter of a triangle is greater than the sum of its three medinas. 2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD. Which of the above statements is/are correct?


  • Options
  • A. 1 only
  • B. 2 only
  • C. Both 1 and 2
  • D. Neither 1 nor 2

  • Correct Answer
  • Both 1 and 2 

    Explanation
    Let ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively.
    Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered)
    Hence in ?ABD, AD is a median
    ?
    AB + AC > 2(AD)
    Similarly, we get
    BC + AC > 2CF
    BC + AB > 2BE
    On adding the above inequations, we get
    (AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE
    2(AB + BC + AC) > 2(AD + BE + CF)
    ?
    AB + BC + AC > AD + BE +CF
     
    2.
    To prove: AB + BC + CA > 2AD
    Construction: AD is joined
    Proof: In triangle ABD,
    AB + BD > AD [because, the sum of any two sides of a triangle is always greater than the
    third side]
    ----
    1
    In triangle ADC,
    AC + DC > AD [because, the sum of any two
    sides of a tri
    angle is always greater than the
    third side]
    ----
    2
    Adding 1 and 2 we get,
    AB + BD + AC + DC > AD + AD
    => AB + (BD + DC) + AC > 2AD
    => AB + BC + AC > 2AD
    Hence proved
    • Tags: Bank Exams

    Volume and Surface Area problems

    Search Results

    • 1. In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?

    • Options
    • A. 2?6 cm
    • B. 3?6 cm
    • C. 3?7 cm
    • D. 6?7 cm
      • Discuss
    • 2. ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right ?angel. What is the area of triangle ADC?

    • Options
    • A. 126 SQ.CM
    • B. 124 SQ.CM
    • C. 122 SQ.CM
    • D. 120 SQ.CM
      • Discuss
    • 3. In ?PQR, ?QPR = 45° and the bisectors of ?PQR and ?PRQ meets at O. What is the value (in degrees) of ?QOR?

    • Options
    • A. 107.5
    • B. 112.5
    • C. 117.5
    • D. 122.5
      • Discuss
    • 4. A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm2) in the total surface area ?

    • Options
    • A. 77
    • B. 154
    • C. 87
    • D. 38.5
      • Discuss
    • 5. The length of the common chord of two intersecting circles is 12 cm. If the diameters of the circles are 15 cm and 13 cm, then what is the distance (in cm) between their centers?

    • Options
    • A. 7/2
    • B. 7
    • C. 7?2
    • D. 14
      • Discuss
    • 6. What is the percentage decrease in the area of a triangle if its each side is halved?

    • Options
    • A. 75%
    • B. 50%
    • C. 25%
    • D. No change
      • Discuss
    • 7. If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

    • Options
    • A. 1 cm or 7 cm
    • B. 2 cm or 14 cm
    • C. 3 cm or 21 cm
    • D. 4 cm or 28 cm
      • Discuss
    • 8. The co-ordinates of the centroid of a triangle ABC are (-1 , 4). What are the co-ordinates of vertex C if co-ordinates of A and B are (-3 , -1) and (3 , 5) respectively?

    • Options
    • A. (-3 , 8)
    • B. (3 , 8)
    • C. (-3 , -8)
    • D. (3 , -8)
      • Discuss
    • 9. What is the reflection of the point (-4, 3) in the line x = -2?

    • Options
    • A. (-4 , -7)
    • B. (4 , 3)
    • C. (0 , 3)
    • D. (-4 , 7)
      • Discuss
    • 10. ?XYZ is similar to ?PQR. If ratio of Perimeter of ?XYZ and Perimeter of ?PQR is 4:9 and if PQ = 27 cm, then what is the length of XY (in cm)?

    • Options
    • A. 9
    • B. 12
    • C. 16
    • D. 15
      • Discuss

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