MathematicsChoose the correct answer:In this figure AOB is a quarter circle of radius 10 and PQRO is a rectangle of perimeter 26. The perimeter of the shaded region is

Choose the correct answer:


In this figure AOB is a quarter circle of radius 10 and PQRO is a rectangle of perimeter 26. The perimeter of the shaded region is


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  1. A
    13+5π1
  2. B
    17+5π
  3. C
    7+10π
  4. D
    7+5π 

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    Solution:

    The correct answer is: 17+5π.
    We know that length of arc BA  is  1 4 2×π×10  
    BA  =5πcm  
    Perimeter =BR+RP+PA+ AB  
    We know that length of both diagonals of the rectangle is the same, therefore, OQ = RP
    Therefore, RP=10cm  
    Perimeter of rectangle:
    RO+OP+PQ+RQ=26cm  
    Now, opposite sides of a rectangle are the same
    So, 2(RO+OP)=26 RO+OP=13cm  
    Now,
    BR+PA=(BORO)+(OAOP) BR+PA=BO+OA(RO+OP)  
     BO=OA=Radius of circle=10 cm
    BR+PA=20(13) BR+PA=7cm  
    Perimeter of shaded region: BR+RP+PA+ BA  
    Perimeter of shaded region =5π+10+7  
    Perimeter of shaded region = 17+5π cm  
    The answer is option 2.
     
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