1) A right triangle is inscribed in a circle with a diameter 100 units long. What is the maximum area of the triangle, in square units?

Let S be the union of the set of all points inside a regular nonagon with side length 2 units and the set of all points less than 1 unit away from a point on the perimeter of the nonagon. What, in units, is the perimeter of S?

Guest Mar 15, 2017

#1**0 **

1) A right triangle is inscribed in a circle with a diameter 100 units long. What is the maximum area of the triangle, in square units?

Note that we can lay the hypotenuse of the right triangle along the diameter of the circle. And the height of this triangle will be the radius of the circle with the two legs being equal.......so......the max area will be = (1/2)B*H = (1/2)D*R = (1/2)(100)(50) = 2500 units^2

Let S be the union of the set of all points inside a regular nonagon with side length 2 units and the set of all points less than 1 unit away from a point on the perimeter of the nonagon. What, in units, is the perimeter of S?

The perimeter is comprised of 9 segments of length 2 plus the circumference of a circle with an radius of 1 [each curved part pf S is 1/9 of this circumference and there are 9 of them ]

The perimeter = 9*2 + 2pi (1) = 18 + 2pi ≈ 24.28 units

CPhill
Mar 15, 2017