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A semicircle is inscribed inside a rectangle in such a way, so that the diameter of the semicircle coincides with the length of the rectangle. If the area of the semicircle is 50 π, then what is the area of the rectangle?

A semicircle is inscribed inside a rectangle in such a way, so that the diameter of the semicircle coincides with the length of the rectangle. If the area of the semicircle is 50 π, then what is the area of the rectangle? Correct Answer 200

GIVEN:

Area of the semicircle = 50 π

Length of rectangle = diameter of the semicircle

CONCEPT:

Here the width of the rectangle is equal to the radius of the semicircle because the diameter of the semicircle coincides with the length of the rectangle.

FORMULAE USED:

Area of semicircle = π × (diameter of the semicircle)2/8

Area of rectangle = length × breadth

CALCULATION:

Area of semi circle = 50π

50π = π × d × d / 8

⇒ d = 20

⇒ Length = diameter = 20 m

∴ Area of rectangle = 20 × 10 = 200

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