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Question

The given figure is formed by 2 quarter circles and the area of the shaded square is 49 cm2. Find the perimeter of the figure. (Take π=227)

A
94 cm
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B
108 cm
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C
86 cm
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D
122 cm
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Solution

The correct option is D 122 cm
Let us assume the side length of the square as x cm.

Area of the square =49 cm2
x2=49x=7
Therefore, the side length of the square is 7 cm.

The radius of the quarter circles =14+x=14+7=21 cm

Marking A, B, C, D, E, and F as the vertices of the given figure.
Perimeter of the figure = AB + Arc BC + CD + DE + Arc EF + FA
=14+(14×2×227×21)+14+14+(14×227×21×21)+14
=56+33+33
=56+66
=122 cm

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