Question

in figure the ratio of area of the quarter circle to that of inscribed rectangle is 50π:21. if the radius of quarter circle is 5cm, then the perimeter of the rectangle is

Answer 1

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Here is your answer

The ratio of area of quarter circle to inscribed rectangle is 50π : 22
Let the area of quarter circle = 50π x
And Area of the rectangle = 21x

Radius of quarter circle = 5 cm

Area of quarter circle is = π r^2/4
$50\pi = \frac{\pi \times 5 {}^{2} \times x}{4} \\ x = \frac{50 \times \pi \times 4}{\pi \times 25} \\ x = 8$
So Area of rectangle = 21× 8
= 168 Sq. cm

Hence Area of inscribed rectangle is 168 sq.cm

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Answer 2

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Here is your answer
Let the Area of quarter circle = 50πx
and Area of rectangle is 21x

Radius of circle is 5 cm

Area of quarter circle = πr^2/4
$50\pi \times x = \frac{\pi \times {5}^{2} }{4} \\ x = \frac{25}{4 \times 50} \\ x = \frac{1}{8}$
Area of rectangle = l× b
$21 \times \frac{1}{8} = 5 \times breadth \\breadth \: = \frac{21}{8 \times 5} \\ b = 0.525$
Therefore, Breadth is 0.525cm

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