Find the area of equilateral triangle with radius length of 8. PLEASE answer in simplified radical form

16√3 units²

Step-by-step explanation:

I believe you meant, "with side length of 8."

Such a triangle has three equal angles, all 60 degrees.  Using this fact we can find the height of the triangle when the bottom side is horizontal:

sin Ф = (opposite side) / (hypotenuse), which here is

sin Ф = (height of triangle) / (8 units), from which we learn that

(height of triangle) = (8 units)(sin 60 degrees) = 8(√3)/2 = 4√3

Now we have all the information necessary to find the area of this triangle A = (1/2)(base)(height)  =  (1/2)(8 units)(4√3 units)  = 16√3 units²

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

idk

step-by-step explanation: