Posted by **Stuck** on Tuesday, March 9, 2010 at 10:25pm.

"A rectangle is inscribed in a semicircle of radius 2 cm. Find the largest area of such a rectangle".

There is a diagram, but I think the question makes it clear enough what is going on. I'm having problems finding a relationship that I can work with.

- Calculus -
**Reiny**, Tuesday, March 9, 2010 at 10:45pm
draw a radius from the centre to a vertex of the rectangle

Let the base of the rectangle be 2x, making the triangle base x, and let the height of the rectangle by y

Area of rectangle = 2xy

but x^2 + y^2 = 4

y = √(4 - x^2) or (4-x^2)^(1/2)

A = 2x(4-x^2)^(1/2)

take the derivative using the product rule,

set it equal to zero and solve for x

- Calculus -
**Stuck**, Tuesday, March 9, 2010 at 11:21pm
Thank you! Never occurred to me to position the radius like that.

## Answer this Question

## Related Questions

- Calculus - Find the rectangle of largest area that can be inscribed in a ...
- Calculus - Find the area of the largest rectangle that can be inscribed in a ...
- Calculus - Find the area of the largest rectangle that fits inside a semicircle ...
- maths - Find the area of the largest rectangle that can be inscribed in a ...
- Calculus - Hello, could someone please help me with this problem? I'm a little ...
- calculus - A Norman window has the shape of a semicircle atop a rectangle so ...
- calculas - find the perimeter of the rectangle with maximum area that can be ...
- Calc - A rectangle is to be inscribed in a semicircle of radius 8, with one side...
- 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 ...

More Related Questions