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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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A. 13+5π
B. 17+5π
C. 7+10π
D. 7+5π

Answer
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Hint: We will be using the concept of mensuration to solve the problem. We will use a formula for finding the perimeter of the circle to find the length of the quadrant and then we will find the length of the diagonal of the rectangle to find the required perimeter.

Complete step by step answer:
Now, we have to find the perimeter of shaded region given as
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Now, we know that the length of arc BA is 14(2×π×10)
=5πcm.............(1)
Now, for the perimeter of the shaded region we have to find the sum of length of BR+RP+PA+AB.
Now, we know that the length of both diagonals of the rectangle is the same.
So, we have OQ = RP. Now, OQ is the radius of the circle. Therefore,
RP=10cm.........(2)
Now, we have the perimeter of rectangle that is
RO+OP+PQ+RQ=26cm
We know that opposite sides of a rectangle are the same. Therefore,
2(RO+OP)=26RO+OP=13cm
Now, we can see from the figure that,
BR+PA=(BORO)+(OAOP)=BO+OA(RO+OP)
Now, BO = OA is the radius of a circle which is equal to 10cm.
Therefore,
BR+PA=20(13)=7cm
Now, the perimeter of the shaded region is BR+RP+PA+arcBA.
Now, from (1), (2) and (3) we have,
=5π+10+7=(17+5π)cm

So, the correct answer is “Option B”.

Note: To solve these types of questions it is important to note the way we have found the length of individual parts and sum them up to find the perimeter of the shaded region also it is very important to note the way we have used the perimeter of the rectangle given to us to find the value of RO+OP.