In the 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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13+5π

17+5π

7+10π

7+5π

answer is B.

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Detailed Solution

It is given that AOB is a quarter circle and PQRO is a rectangle in the quarter circle
It is clear from the diagram that the radius of the quarter circle is the diagonal OQ of the rectangle OPQR. So,

Now, as given in the question, the perimeter of the rectangle OPQR is 26.

and

Now, to find the perimeter of the shaded region, we add the perimeters of line PA, arc AQB, line BR and line RP.
∴ Perimeter of shaded region

and

Thus, perimeter of shaded region
Question Image

We have perimeter of shaded region

(option 2)
So, option 2 is correct.

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