PQRS is a rectangle in which lenght is two times the width and L is the mid point of PQ. with P and Q as centre's draw two quadrants. find the ratio of the area of the area of the rectangle PQRS to the Area of shaded region
Answers
Let breadth of rectangle PQRS = x , As given length is two times of breadth so Length of rectangle PQRS = 2 x
We know area of rectangle = Length × Breadth , So
Area od rectangle PQRS = 2 x × x = 2 x2
As given " L " is mid point of PQ , So PL = QL = Radius of quadrant = x ( Same as breadth as we know breadth is half of length )
We know area of quadrant of circle = π r²4 , So
Area of given quadrant of circle = π x²/4 , Then
Area of both quadrant of circle = 2 ( π x²/4 )
= π x²/2 = 22/7 × x²/2
= 22× x²/14= 11 x²/7
Thus,
Area of shaded region = Area of rectangle - Area of both quadrant of circle
= 2 x² - 11 x²/7
= 14 x²−11 x²/7
= 3 x²/7
Then,
Area of rectangle PQRS/Area of shaded region
= 2 x²/3 x²/7
.
= 14 x²/3 x²
= 14/3
Therefore,
Area of rectangle PQRS : Area of shaded portion = 14 : 3 ( Ans )
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