# A rectangle of the largest possible area is cut out from a semi-circle of perimeter 72 cm

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A rectangle of the largest possible area is cut out from a semi-circle of perimeter 72 cm. What is the area of the rectangle cut out? ( Take n = 22 / 7 )

1. 196 cm 2
2. 156.8 cm 2
3. 210 cm 2
4. 528 cm 2

It's 196cm^2.
Required area is equivalent to finding the area of largest possible triangle that can be inscribed in the semi circle.
The largest possible triangle that can be inscribed inside a semicircle is the right angled triangle whose hypotenuse is the diameter of the semicircle, and whose other two sides are equal.
The area of the largest triangle that can be inscribed in a semicircle of radius r = r^2.
Radius of the semicircle is 14cm. (perimeter of semi-circle = 2r + 22r/7 = 72)
So 14^2 = 196cm^2.
1.196

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