Friday

January 30, 2015

January 30, 2015

Posted by **Anonymous** on Tuesday, December 7, 2010 at 9:51pm.

- calculas -
**Reiny**, Tuesday, December 7, 2010 at 10:06pmDid you make a sketch?

draw a line from the centre to a vertex of the rectangle lying on the semicircle.

Let the length of the rectangle be 2x and its height y

I see a right-angled triangle with sides x and y and hypotenuse 2

x^2 + y^2 = 4

let the area be A

A = 2xy

A^2 = 4x^2y^2 = 4x^2(4-x^2)

= 16x^2 - 4x^4

2A dA/dx = 32x - 16x^3 = 0 for max of A

16x(2 - x^2) = 0

x^2=2

x=√2

sub back into equation above

y = √2

so length = 2√2 and width = √2

Perimeter = 6√2

- calculas -
**Anonymous**, Tuesday, December 7, 2010 at 10:10pmthank you so muchh :)

**Answer this Question**

**Related Questions**

Calculus - A rectangle is constructed with its base on the diameter of a ...

calculus - A rectangle is constructed with its base on the diameter of a ...

pre-calc - a semicircle of radius r=3x is inscribed in a rectangle so that the ...

Calc - A rectangle is to be inscribed in a semicircle of radius 8, with one side...

Calculus - Find the rectangle of largest area that can be inscribed in a ...

Optimization - A Norman window has the shape of a semicircle atop a rectangle so...

solid mensuration - Find the area of a portion of a semicircle of radius 15 m ...

math - A Norman window has the shape of a rectangle surmounted by a semicircle...

maths - Find the area of the largest rectangle that can be inscribed in a ...

Calculus - Find the area of the largest rectangle that can be inscribed in a ...