Find the rectangle of largest area that can be inscribed in a semicircle of radius r, assuming that one side of the rectangle lies of the diameter of the semicircle. what is the length of the smaller side of the rectangle? what is the length of the larger side of the rectangle?

Please refer to the attached figure.

If the circle has radius , the semicircle has equation , defined for .

The coordinates of the points are:

This implies that

So, the area of the rectangle is the product of the width and the height. We want to find the maximum of

To do so, let's start by computing its derivative:

The derivative equals zero if the numerator equals zero:

So, we have

the correct answer is semicircle

step-by-step explanation:

the answer is semicircle because the shorter arc joining two points on the circumference of a circle is known as the minor arc, the larger arc is called the major arc, and a semicircle is a half circle, formed by cutting a whole circle along a diameter line.

hope i .

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680