Let f be a point of a rectangle, ∠FOB = x, R stands for radius, cosb = (root number 5)/5, sinb = 2* (root number 5)/5.

The area of this inscribed rectangle is (r * sinx) * (2 * r * cosx) = r 2 * sin (2x) < = r 2 (when sin2x = 1 is true).

The perimeter of the inscribed rectangle is: 2 * (r * sinx+2 * r * cosx) = 2 * r * (sinx+2cosx) = 2 * r * sin (x+b).

Let r = 5 wait for the first question, and r = R get the third question.

2:

Let the bottom of the water tank be a in length and h in height.

De: a*a*h = 256

Y = a * a+4 * a * h = 256/h+4 *16 * h = 256/h+2 *16 * root h > = 3 * (256/h) * (2 */kloc-0

When 256/h = 2* 16* root sign, the equal sign holds, and h= 4.